Play: Specifically means if a player stages and plays the card.

Eg: If Sakaar puts Star-Lord from your hand to its location, his On Reveal effect will go off. However, since your opponent didn’t Play a card there, it will fail, and he will not get +3 Power.

Add: Creates a card at a location, but will not trigger any “Play” effects.

Eg: If a player plays Squirrel Girl and the opponent plays Star-Lord at a different location, Star-Lord won’t activate based on the generic Squirrel token.

Put: Similar to Add, it just places a card on the location specified without activating “Play” criteria.

Move: Some cards (like Nightcrawler) can move to another location.  

If a card says that something happens when it moves, anything moving it can trigger its ability.  Eg: Vulture gets enhanced when it’s moved by either player or a location.

Example: Bar Sinister doesn't play extra cards at the location, but subsequent cards do copy the previous card’s stats and any On Reveal effects can take place.  Try playing Medusa on Bar Sinister when it is the middle location!