Jump

The trademark move of the whole Marioverse. This move is is easily recognizable to all, even people who have not played any of the games.It elevates a character temporarily in the air when on the floor. In the platformers you can break and activate blocks by hitting them from underneath during a jump. In some sidescrollers, you had to be normal Mario to break bricks. There are many variations to this move. The height and width of the jump varies on the game and character. On the Mario Party Series all of the characters jump to the same height, thought the short(Ex.Toad) characters technically jump higher because they jump to the same height as the tall (Ex.Waluigi) characters.

Pretty much anything with legs can use it. Even characters without legs, like Boo can use it. Mario was also the first to use it. Donkey Kong was the first game it has been used in and also the first game in the Marioverse. It has appeared in almost every Mario game to date. It was also the first game with a jump action.

Stomp
Stomp is the second part of a Jump while coming down. You don't have to Jump, you can also fall off a ledge or cliff. If you Stomp on top of an enemy or switch you can either kill/hurt the enemy or activate the Switch. You can Stomp on many enemies, though it doesn't work on spiked and fire enemies and can return damage. Boo is an exception because you can't Stomp on him in the Mario sidescrollers, but you can in the rest of the games.

Anyone who can Jump can Stomp. In the Mario Rpg Series you use it with a Timed Hit for extra damage. In Mario Party Series you can jump on rival to stun them briefly, though it is still not as strong as a Ground Pound.