These are the 2 most common types of buttercream I believe.
American buttercream is made with butter and or shortening with powdered sugar, and flavorings. Sometimes meringue powders, dream whip, or other additions are also made. It is quick, easy, has a long shelf life, and may be "crusting" (gets a firm dry crust).
Meringue buttercreams are made with whipped egg whites. Swiss meringue and Italian meringue buttercreams are very similar. They contain egg whites, butter and sugar, plus flavorings In IMBC a very hot sugar syrup is poured into whipped egg whites, then butter is added. In SMBC, the whites and sugar are heated and dissolved then whipped before adding the butter.
My personal favorite is SMBC. A little more work than ABC, but worth it. I can whip up a batch pretty quickly now, and it freezes beautifully, ABC is very sweet, and I use it mostly for kids cakes. Sometimes I mix SMBC and ABC 50/50 if I can't decide which way to go. The meringue BCs are more flexible in what can be added, and have a lighter less sweet taste. Add a little liqueur and they are even better! The egg whites are pasteurized by the heating process, but the shelf life is not quite as long as ABC. I don't know what the official word is, but I have left it out for 24 hours without a problem (not outdoors in the heat).
This has an excellent SMBC tutorial. It is by a cc Moderator (the better white cake on the same site is also wonderful)
This is an ongoing CC discussion about BC