This varies by site and context. "Simulation" tends to be the broader term and mainly implies the game focuses on interactive sex scenes or "game-y" gameplay elements (already two distinct concepts...) while not necessarily following a story. A "trainer" meanwhile usually refers to a very specific kind of semi-sandbox time management game in which the player makes mutually exclusive choices to raise some measure of sexual performance. Most of the time the MC is put in a position of power over a single (usually female) sex interest at a time with little to no romantic relation between the two and plans out a daily/weekly schedule for the trainee to follow.
