The answer really depends on the context, but "forget about it" can be used (1) when you are asking someone not to worry about something, or as you said, (2) to stop a topic you no longer wish to pursue. In slang, "forget about it' is (3) also used as a response to something unbelievable. Ex: Peter: I still owe you $2 from last week. Paul: Forget about it (meaning, don't worry about it, you don't have to pay me back) Ex 2: Peter: How much money did you make yesterday? Paul: Forget about it (meaning, I don't want to talk about it, or don't mention it). Ex 3: Peter: I ate 36 hot dogs in one sitting! Paul: Forget about it! (meaning, "unbelievable!") Actually, "forget it" is just a shortened version of "forget about it," so it has the same meaning. The terms can usually be used interchangeably. Of course, if you say "I forget it" (using the subject "I"), then the sentence can mean "I can't remember something." But in this case, Americans usually say "I forget" rather than "I forget it." Note that "forget about it" is rather informal and is primarily used between friends, so you wouldn't say it to your boss, for example.

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