Most Helpful Guy
Putting games into categories has always been tricky. Plus games tend toward one-size-fits-all these days. By these days I mean over the last 15-20 years.
RPG is Role Playing Game. There is usually some sort of story. Some people like me completely ignore the story. The game play itself is focused on character building. So the player levels up and develops the character with new or improved skills. Also weapons, armor and magic are important.
Adventure is a genre that has seriously changed over the years. I started playing them almost 40 years ago. They used to be almost entirely about exploring and doing quests. Like a real life adventure. There was very little to no character development. The only "reward" for completing quests was simply enabling you to move forward in the game. The quests tended to be puzzle-like. Nowadays I don't think there are any true adventure games. Adventure has become more of a marketing label than anything else.
Action games mean skill based. There are fast paced real time games. Traditional RPGs were almost always turn based games, similar to playing chess. Action games on the other hand are more like fast paced arcade games.
Classic RPG games are games like the old Might and Magic games. A little newer would be the Baulders Gate series. Also Morrowind and Skyrim and somewhat hybrids.