I'm sure all of these are covered by Wikipedia ;-) but I'd like to post my own impressions of what the different terms mean. I don't claim to be the world's leading expert, so everyone feel free to correct me, clarify, and add to this list.
faithful Mormon, believing Mormon, true-believing Mormon (TBM): Someone who believes in Mormonism and practices it (especially the SLC-based LDS church). Typically has a "testimony".
active Mormon: Someone who attends LDS church regularly -- at least once a month -- and fulfills callings.
inactive Mormon: Someone who is listed as a member on the LDS church records but is MIA as far as the LDS church is concerned. Theoretically this applies mostly to people who might be "reactivated", however in practice it could be anything. Including dead.
jack Mormon, jackmo: Someone who believes in Mormonism but does not practice. This term is especially applied to believers who ignore important commandments such as the "Word of Wisdom" and the "law of chastity."
New Order Mormon (NOM): Someone who disbelieves key doctrines of Mormonism yet actively chooses to practice Mormonism.
Liberal Mormon: Somewhere between the "when the prophet speaks, the thinking has been done" crowd and the New Order Mormons. Includes many TBMs as well as many readers of the magazine Sunstone.
Bloggernaccler or Naccler: Soumeone who regularly frequents the LDS-themed blogs. On average, they tend to be liberal Mormons.
Utah Mormon: A Mormon from Utah. Amusing stereotypes abound, especially involving funeral potatoes, "creative" first names, and saying "Oh my heck!"
mission-field Mormon: A Mormon who grew up or lives in a place with hardly a Mormon in sight.
exmormon, exmo, ex-Mormon: Someone who used to believe in Mormonism but doesn't anymore. Usually excommunicated or "resigned" but not necessarily.
post-Mormon: Same as exmormon. This term is sometimes preferred by those who feel that the term "exmormon" has negative connotations.
anti-Mormon: Someone who deliberately opposes and fights against the LDS church.
fundamentalist Mormon or Mormon fundamentalist: A member of one of the sects that broke from the SLC-based LDS church over the doctrine of polygamy. (The LDS church discourages use of this term, but it is commonly understood in practice.)
apostate: Someone who has fallen away from the church. There is some confusion as to precisely who fits into this category. Whether it's exmormons, anti-Mormons, fundamentalist Mormons, members of the SLC-based LDS church, or people who have fallen away from some entirely different religion really depends on who you're talking to...
ethnic Mormon: A multi-generational Mormon, especially a descendant of Mormon pioneers and/or polygamists.
(Mormon) convert: Someone who converted to Mormonism from some other religion or world-view.
Community of Christ, Strangite, Bickertonite, etc.: I don't know all of the terms for the members of other restoration churches -- any help would be appreciated.
cultural Mormon: All of the above.