We classify FKT attempts as supported, self-supported, and unsupported, and call this classification "style":
Supported means you have a dedicated support team that meets you along the way to supply whatever you need. This generally allows for the fastest, lightest trips, and for an element of camaraderie and safety, since someone knows about where you are at all times.
Self-supported means that you don't carry everything you need from the start, but you don't have dedicated, pre-arranged people helping you. This is commonly done a couple different ways: You might put out stashes of supplies for yourself prior to the trip, or you might just use what's out there, such as stores, begging from other trail users, etc. Long distance backpackers are typically self-supported, since they resupply by mail drop or in stores. A subset of self-supported style has become the standard for some of the longer thru-hiking routes, such as the AT and PCT. We'll call this the Williamson Standard, since it was first clearly articulated by Scott Williamson (see the PCT thread on the old Proboards site.) Williamson said (in part):
"I will NOT have anyone following, or otherwise meeting me in prearranged manner to give me support. I plan to do this hike ... as a backpacker, carrying all of my food, equipment, and water [note that using natural water sources along the route is allowed] between resupply towns, which I will walk into and out to pick up prepacked and mailed food boxes or purchasing food, in these towns. ...I will not be getting in a vehicle for any reason during this attempt, if I do it means the attempt is off. I will be following the official PCT route, no detours, road walks or alternates of any kind. For me the style of this undertaking is more important than breaking the record itself."
Unsupported means you have no external support of any kind. Typically, this means that you must carry all your supplies right from the start, except any water that can be obtained along the way from natural sources. The longest trip I'm aware of using this style is Coup's 20-day thru-hike of the Colorado Trail. For most people, carrying enough food for more than a few days to one week will be prohibitive. Unsupported also means unaccompanied! (i.e., no pacers)
Can a "team" be considered unsupported?
It's controversial. Further note: Some people get really crazy about what does or does not fit into "unsupported". I've had long conversations about this especially with Jeff List, who very thoroughly documented the opinions expressed here.