"All I want" means "the only thing" (or things) I want. So, what you want in this case is limited. In your first example this is limited to peace and quiet, in the second example, only one thing is wanted: love. "Everything" however is not limited: this means that you want all things. Imagine you go out for a big meal in a restaurant, with many dishes. One person might say "All I want is a bit of fish and some ice cream - just those two things". Another person might say, "I'm so hungry. I want everything. I want to have a taste of everything." (So, no limits for this person). If it were a Chinese restaurant, I would be the second person 😉..

Both sentences would use “ALL”

That’s actually a very good question, Patryk, and not an easy one to answer. Native English speakers get a sort of feel for which one sounds right in a sentence, and which one doesn’t, but when asked why, it’s probably going to be difficult for him or her to say why. First off, the proper expression is „All I want is peace and quiet.“ And „All you need is love“ is correct (in fact those are the words to an old Beetles song). The answers the others gave are all good, but this is my take on it: All presupposes a limited number of some sort, where everything sounds unlimited. Like, say a person writes a report and cites 10 points and says many other things. You might criticize the report by saying „all the 10 points he makes are wrong, but not everything in the report is wrong (there’s more to the report than just the 10 points for example).“ It‘s not a perfect answer, but that’s sort of the feel I have for it. The two are quite close in meaning. Like in your question, „all I want is peace and quiet“ is an example of naming just 2 things you want. A limited number. Peace and quite are not everything there is to have in the world. Everything you need is love doesn’t work, probably because it’s not factually correct anyway. There’s more to what you need (I guess to exist) than just love. Hence, all I need works because you are focusing on just one thing. Good question and a hard one to answer.

Hey Patryk, I had to think about this question a bit. I'm going to try to give you some sentences in context. It might help to think of them by their grammar structures. "All" can be a pronoun, determiner/predeterminer, an adverb, or a noun. And "everything" is a pronoun that means: "all the things". How many things do I want? I want all the things -> I want everything does all of that make sense? did you understand all of that? does everything make sense? did you understand everything? for your sentences and how I interpret their differences: Everything I want is peace and quiet -> this is describing an unknown number of things(but includes all of them) that have a characteristic of peace and quiet. All I want is peace and quiet -> stating that the only things you want are some peace and some quiet.

The words mean the same thing, but we tend to us them in certain phrases. For example, the phrases 'All I want...', 'All we did..', are a standard way speaking and mean 'the only thing I want', etc. However, we say 'all the cars', or 'all the fields', but we cannot say 'everything the...'. Everything is not followed by 'the' or nouns, but we can say 'everything green', or 'everything small'.