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I am confused as to why we say "that is okay" when we don't want someone to do something. For example,
A: Do you want a hotdog?
B: That's okay.
I would think that the means that it is okay to do, since you are saying that it is, quite literally, okay.
What is being said:
Q: Do you want a hotdog?
A1: I'm okay/That's okay. Thanks.
A2: I'm good/I'm cool/I'm fine. A3. That's OK. Thanks
What isn't being said, but might be implied:
Q: Do you want to change your present situation by adding a hotdog to it?
A1: I'm okay the way I am. Thank you for offering to give me a hot dog.
A2: My present situation is good/cool/fine.
Note that all of these responses (I'm okay, I'm good, I'm fine, I'm cool) are casual speech, to varying degrees. I would use them with my friends, or my employer, but maybe not with my prospective employer. For example, in a job interview, I might say I'm fine, thank you but not I'm cool, thank you. If the president offered me the hotdog, I would either just say No thank you, or, most likely, accept the hot dog.
Note: This usage of I'm OK is fairly common in the U.S. (At least on the west coast.) To my ear, it is virtually interchangeable with "That's OK." @DavidRicherby indicates in the comments above and below that "I'm OK" is used in British English, but "That's OK" is not (at least not in this sense.)
Usually, that's okay (or it's okay) is a phrase often used in the sense of don't worry about it, it's not a problem etc. For example:
- A: I'm so sorry I scratched your car!
- B: That's okay, don't worry about it.
In the example sentence you have given, people would more often say I'm okay, which is the same as I'm good and is basically just an indirect and polite way of saying no, thank you. Example:
- A: Would you like a hotdog?
- B: I'm okay, thanks.
B's answer might just as well have been:
No, thank you, I'm good.
The I'm good is not necessary in the sentence, but I hope you get the point that there are many different ways of formulating the meaning of B's answer.
The meaning can almost always be understood based on the context, but you're right in thinking there can be ambiguous usage. Here is an ambiguous example.
Cashier: Would you like a plastic bag?
Customer: That's okay.
Written out, this might look like the customer is accepting the bag, but if it's said with the right inflection, it can sound like s/he is declining.
In your example, I like to think of "that's okay" as an abbreviation of this response:
A: "Would you like a hot dog?"
B: "No, you can keep it and that's okay."
In other words, it could be said that B is expressing that they won't be upset if they don't get the hot dog from A.
I think if B does not want a hot dog, she will say
No thanks. That's okay.
Which means, no thanks (and it's fine with me that you get one, even though I don't want one).
I think it’s in the meaning of that or it are prounouns used to describe their state of being regarding the item spoken for example “do you want some cake” the reply of “that/it’s ok” would be a shortened form of “that state of being (referring to having enough cake) is satisfied” or “it (referring again to said state of being) is satisfied”
