There are three main types of Marty Stu:
a) Classical!Marty-Stu. Think 50s and 60s sitcoms or the beginning of the movie "Pleasantville". These are usually your blonde haired, blue eyed, stereotypically gorgeous, pretty boys. They also tend to be fond of sports and be "jocks" or "preps".
b) Rebel!Marty-Stu. Also known as "Punk!Non-conformist!Marty-Stu", "Goth!Marty-Stu" and "Badass!Marty-Stu". This type of Marty-Stu usually has agnst coming out of his you-know-what and isn't *really* badass, he just wants to be because he's oh!-so-angry about his tragic past. Blah, blah, sob story, mush. This type is often written by teenage girls around the age of 13-15, and is extremely loud and obnoxious. It also includes Evil!Stus.
c) Misfit!Marty-Stu. This encompasses all of the Marty-Stus out there that the authors have made short, scrawny, geeky, etc in an attempt to prove that he's "not a marty-stu!!!one1". Usually has a tragic past where he was bullied and/or abused terribly. This type is usually a bit less obnoxious than the other two. Occasionally, this type will also be an Evil!Stu, but that is very rare. It often includes the "I'm a very sensitive person but my father/parents/brothers/family/society doesn't like that in a boy so I get ostracized"-type Marty-Stu. These are usually the ones that wind up in slash fics.
or becomes romantically envolved the author's favorite canon characters. He can also closely resemble any canon character.
The name of the character referred to as the "Marty-Stu" does not matter.