http://www.wizards.com/default.asp?x=judge/resources/bannedthose are your basic formats. the constructed and eternal are the ones supported by the DCI (people who organise tourneys), though the eternal formats significantly less so, while the online formats are options you can select for your games on mtgo, and tournaments with them aren't supported outside of the program.
also, two-headed giant isn't it's own format, you play two-headed giant block, or two-headed giant standard, or even two-headed giant limited, etc. and add the banned lists together.
edit: oh, one last thing. while they give the format names on that page, they used to be just different types of tournament play, and some people still call the formats type [whatever] or t[whatever] for shorthand. if you're unaware:
t2 = standard
t1.x = extended
t1.5 = legacy
t1 = vintage
t1.x is the least used of the four, but there they are.