Could you please tell me the difference between these two sentences and what they mean?
- My girlfriend always thinks I am cheating on her.
- My girlfriend always thinks I cheat on her.
The use of the present progressive indicates an ongoing situation. In this case it implies she thinks you are currently cheating on her, probably with one, specific person.
In contrast, the simple present indicates a regularly occurring situation, something that you do over and over. Not necessarily in the current moment, but something you can be expected to do. So if she always thinks you cheat on her, that implies you do so from time to time, can be expected to do so again, and not necessarily with the same person.
I am eating lunch at noon.
I eat lunch at noon
The first sentence implies I will have lunch today but not necessarily at the same time every day. The second says that I usually eat lunch at noon, every day -- that it is a regular, expected event.
However, your examples are nuanced by the word "always", which also implies a recurring situation. So both actually end up meaning more or less the same thing -- that your girlfriend thinks you cheat on her regularly, and with different people.
[Edit] In informal conversation, the use of "always" here does not actually mean "all the time" but rather implies "more frequently than I like". So you would use it to indicate unwanted behavior. Examples:
That salon always charges me too much to cut my hair.
These shoes are always so tight when I first put them on.
Many English words like "always" or "totally" are used figuratively to imply something different from their actual meaning. Sometimes you have to interpret the meaning from context.
My gf always thinks I cheat on her
From time to time your girlfriend thinks you cheat on her. There are periods of time where she doesn't.
Or, your girlfriend thinks you are cheating each time you do something X - the X would have to be from context or earlier stated. You may or may not be doing X now.
My gf always thinks I am cheating on her