Keirsey bases type on just the four letters - like INFJ or ISTP - without any discussion of which functions are being used, and holistic type descriptions. That means I'm Introverted Intuitive Feeling Judger, but not that I have Fe or Ni.
Function theory, on the other hand, explains more subtle behaviors on strength of functions, which some people prefer as being more accurate, finding Keirsey over-simplified. Then again, people who prefer Keirsey think that function theory is too convuluted and difficult to prove, because of sketchy definitions, and the simple fact that although you may recognize functions within yourself, it's pretty hard to prove in other people. In fact it's quite presumptuous to assume you know what motivates another person, since functions aren't supposed to be based on outward behavior, but motives for outward behavior.
Some people take function theory so far that I think it's insane. On the other hand, Keirsey does lack subtlety, and attempts to put people in just sixteen plain little boxes.
I'm definitely INFJ in Keirsey because I test it over and over and over again, and have for years on Keirsey type tests, and when someone from this web site who prefers Keirsey met me, he confirmed that he believes I'm INFJ.
HOWEVER, if you asked anyone else on this forum if I'm INFJ - well at least anyone who subscribes to function theory - they'd probably laugh at you, insisting that I clearly use Ne/Fi/Te/Si, and I'd kind of have to agree.