FBS is Football Bowl Subdivision. This was called Division 1-A when it came into being in 1978; its name was changed to FBS in 2006.
FCS is Football Championship Division. This was Division 1-AA from 1978 to 2006.
FBS schools are allowed to have 85 student-athletes on football scholarship at any one time. These are all full-ride scholarships. FCS schools are allowed the equivalent of 63 full scholarships. Some of the 63 can be divided up into partial scholarships at a school’s discretion as long as not more than 85 players are receiving financial aid at any given time.
FBS schools must meet an attendance requirement for home games: 15,000 on average. This is actual or paid attendance. There is no such requirement in FCS.
FBS teams can play 12 regular season games. FCS teams will play only 11 games in 2015 after being allowed 12 games in 2013 and 2014.
The playoff in FBS is for four teams only. In FCS it is currently up to 24 teams.
An FBS team becomes “bowl-eligible,” meaning it can play in a bowl game if invited, by posting a .500 or better season record. In the typical 12-game season, that would be 6-6. If a team plays 13 games, it would need seven wins. Only one of the required wins can be against an FCS opponent, so a team needs to beat at least five FBS opponents. This effectively eliminates FCS schools from bowl consideration.