Never played a MH game so I'm lost here. Guessing you run around and kill monsters, basically.
Yes and no, MH is a quest/mission based game in a similar style to Phantasy Star Online, you start off in a village and talk to the guild members for quests a number of which involve hunting marks (monsters), each quest are grouped into ranks, finish lower ranked ones to unlock the next tier. Very simple goal but the game's execution of it is what draws or for many western players repels them, you start off with the bare basics and have to gather materials (some of which only come from monsters themselves) from your hunts to forge better equipment and gear which helps improve your chances in hunts as better equipment comes with better stats, traits and abilities so the is an element of heavy grinding.
MH Generations or X in Japan added a new spin with hunting styles which give you a specialized action and hunter artes (special moves essentially), for example Adept style adds a unique dodge that when activated at the last possible moment allows you to evade an enemy attack and instantly counter.