That's both one of the best, and at the same time, one of the worst aspects of the FF series. You can absolutely fall in love with one installment, but loathe the next one. None of them play the same.
Though the amount of change is usually pretty low with a few exceptions (amusingly enough X is one of the big ones).
I -> II was very different since II is in many ways the origin of the SaGa games rather than final fantasy.
I->III -> IV -> V -> VI -> VII -> IX have relatively minor changes (the major change between I and III is the introduction of the Job System, IV removes the job system but introduces Active Time Battle (and characters with actual personalities), V reintroduces the job system, VI removes the job system , VII greatly expands on the way magic was learned in VI , IX does a similar thing but in a different direction (each character learns unique abilities from equipment).
VII->VIII is actually kinda different (with the way enemies scale, a very different magic system, and the junction system for abilities).
IX->X is a major change being a pure turn based game for the first time since IV.
XII is hard to place, it's different in a lot of ways and similar in others.
XIII trilogy is a pretty major departure again (moving more towards being an ARPG).
XI and IV are MMORPGs.
Long story short: II, VIII, X , XII , XIII are the non_MMORPG ones that are majorly different.