Watch out. The answer is going to be far more complicated than you ever expected, but once you understand it, you will understand something very important about English grammar.
Both sentences mean almost the same thing, and both sentences are strange.
How do your parents punish you this year?
suggests that my parents long ago planned out a schedule of punishments for me, in which the punishment changes each year. Perhaps in 2017, they wrote out the schedule as follows: "2018: Spankings. 2019: Deprivation of supper. 2020: Sit in corner of room. 2021: Sarcasm. 2022: Twenty push-ups." The "How do…?" form of your question is equivalent to "What punishment is designated for 2021 on your parents' punishment schedule?"
How are your parents punishing you this year?
suggests that my parents always punish me the same way, but that they might have punished me one way last year and switched to a different way this year. The "How are…?" form of your question is equivalent to "What is your parents' current way of punishing you?" (plus the suggestion that the punishment might change from year to year). It does not imply that they are punishing me now. It implies only that they now have a standard method of punishment, expected to remain in force for all of 2021.
The strange implications result from the phrase this year at the end of each question. If we remove this from the questions, we might reveal the distinction between the simple and continuous present that you really intended to ask about.
How do your parents punish you?
The simple present tense suggests that my parents have a standard, consistent way of punishing me. This way of using the simple present is for facts that do not have a precise time—facts that are eternal, like laws of nature or mathematics ("Two and two make four"), or facts in force now even if subject to change ("The United States Supreme Court has nine Justices"), such as a parent's policy regarding punishment.
How are your parents punishing you?
The continuous present tense suggests that the punishment is transient in some way: that the present situation is now happening but will be over soon or is now changing or is likely to change.
This last form of the question does not mean that I am now being punished, but it agrees with the premise that I am currently being punished. It also agrees with the premise that a punishment is planned for me but hasn't yet started. It also agrees with the premise that my parents have a current, possibly changing method of punishment, even if I am not being punished right now.
Smokin' in the Boys Room
To understand that, imagine these two situations in which we are talking on the phone:
(1) You heard that I was caught smoking cigarettes in the bathroom at school. The principal informed my parents and left the punishment to them. Now you want to know what it is, so you ask, "How are your parents punishing you?" Here are two possible answers I could give:
I am grounded.
Starting tonight when I get home, I am grounded.
The first answer means that the punishment is happening right at this moment. The second answer means that the punishment is planned but hasn't started yet. Both answers agree grammatically with the question. This is because, in English, the present tense (both simple and continuous) can refer to the immediate present or to the future! The first answer retroactively made your question about a punishment now in progress, which will eventually end. The second answer retroactively made your question about the planned punishment. When the present tense is made to refer to the future, usually by specifying the time explicitly ("Starting tonight"), it means what is now planned or what is now expected. The same thing occurs in conversations like this: "When are you coming to India?" "I fly to Mumbai next week."
(2) You want me to smoke cigarettes with you in the bathroom at school. I am reluctant, because I fear being punished. You want to persuade me not to worry about the punishment, so, to find out what the punishment is, you ask either of these questions:
How do your parents punish you?
How are your parents punishing you?
In this context, these both ask, "What is your parents' method of punishment?" with the understanding that I am not being punished right now. They both imply that my parents have a current method of punishment. They both suggest that punishment, for me, is a pretty frequent occurrence (or else you would say "How would your parents punish you?"). The first question suggests that my parents' method of punishment doesn't often change. The second question suggests that my parents' method of punishment has been changing a lot lately, so the latest information you have about it might be out of date.
This is because the simple present ("How do…?") agrees with a stable fact, not limited to the present moment and unlikely to change soon; and the continuous present agrees with a process that is in progress or a situation that is changing or likely to change.
English tenses are probably starting to sound too complicated to ever master. But notice that I used the continuous present in the preceding sentence. That's about to change.
The main reason that learners get confused is because they think that each grammatical form means a certain thing, so they expect each verb tense to means a certain time (past, present, future, etc.) and a certain aspect (completed, in progress, habitual, etc.). Here is the main lesson: It's the other way around. When people speak in English, they always know which kind of time and aspect they have in mind, but there are many fewer grammatical forms than times/aspects that you must distinguish. They choose the grammatical form mainly to agree with what time/aspect they expect the listener to already understand—or to present new information, such as the clarification in situation (1).
This table shows you the times and aspects and grammatical forms discussed above, plus a few more:
||"War is hell."
|present and stable; subject to change
||"This war is hell." (But it could get better.)
"Do you have a cigarette?"
"The Supreme Court has nine Justices."
||"Do you smoke?"
"I work at a grocery store."
"I fly to Mumbai."
||simple present (with future time specified)
||"I fly to Mumbai next week."
|past state, in a story
||"Julius Caesar is angry."
|past process from beginning to end, in a story
||"A star is born."
|present state; transient, a process in progress
||"Are you smoking?" (i.e. puffing on a cigarette right this second)
|present+habitual but subject to change
||"Are you smoking?" (i.e. currently addicted)
||"I'm flying to Mumbai."
|past state in a story; transient, a process in progress
||"Julius Caesar is becoming too self-important."
Notice that the table lists ten times+aspects and only two grammatical forms.
To understand someone else's speech, you need to keep track of the time+aspect of what they're talking about. English requires every statement to be seen as one of these time+aspects or another. Keeping track of the time+aspect is a big part of how we stay in sync with each other when talking. The other person is always choosing grammatical forms to help you keep track. When they're ambiguous, we add another hint, like "currently" or "starting tonight" or "next week".
To speak grammatically, you just need to provide the same hints to help the other person keep track of the time+aspect that you have in mind. There are only a few hints to choose from! You can put the verb into the present tense ("punish"), or into the past tense ("punished"), or make it a participle with a linking verb ("are punishing"), or add a modal verb ("will punish"). Optionally, you can add an adverb or an explicit time ("currently", "this year"). The main thing is to choose a grammatical form that agrees with the context. In situation (1), if you ask, "How do your parents punish you?", your listener will wonder if there is a misunderstanding, because asking about the standard/habitual punishment doesn't make obvious sense with the current topic of conversation.
The hard thing for most non-native speakers to learn is to always keep track of the time+aspect. You must make a habit of seeing every statement in terms of the English time+aspects. Other languages have different required time+aspect categories or none at all. If you always keep track of the time+aspect, figuring out which grammatical form communicates it to the other person is not difficult.
You don't even need to memorize the table or the names for these things. You can mostly just pick it up from examples, as long as you keep in mind that you are supposed to always guess the time+aspect that the speaker had in mind.
This year again
Now you can see where those strange interpretations at the start of this answer came from. When you add "this year" to a verb understood as present+habitual ("How do…?"), the listener finds a way to make sense of that in terms of the English way of looking at time. "It's present and stable but only this year? I guess maybe it's part of a plan with a new punishment each year."
Similarly, when you add "this year" to a verb understood as present+transient ("How are…?"), the listener finds a way to make sense of that. "It's transient but it lasts for one year?? I guess maybe these parents are always modifying their punishment, but changes only come into effect once a year."