In short, a keeper league allows you to retain players from one year to the next.
How each league goes about accomplishing that is where the distinctions arise:Draft keeper leagues
let you retain a number of players at the expense of draft picks in the subsequent year.Contract/Salary keeper leagues
let you retain a number of players at the expense of your salary cap in the subsequent year.Pure dynasty leagues
let you retain any number of players without no penalty for as long as you want.
Those are the most common variants. I'm sure there are others, but if you have these in your head, you'll have 90% of the leagues covered.