Sprites are individually drawn pieces of artwork for your game which can be absolutely anything. From Trees to Houses, Cars, Buses, Boats or whatever else you can think of.

There separated individually because they usually use some sort of 'Animation' or different colors to make it stand out from the background to show that can be 'interacted' with in some way or that it is an 'Object' that can be manipulated or controlled. 

Most Sprites would be your 'Player' Character, 'Enemy' Character or 'Objects' that you would use, like a 'Lever', which would all have a change in Sprite which would need to be controlled by a function or an interaction to show some kind of 'State' or 'Behaviour' change, unlike Backgrounds which are not something you would normally interact with, however in some cases Sprites are used as Background images, as these can be larger in size and can't be used through a Tile Set.

Sprites with different 'States' or changes 'Behaviour' would normally be found on a 'Sprite Sheet' which hold all the frames for that Sprite. Frames are multiple single image's of the same Sprite which represent a movement which run in a sequence creating an Animation.

These 'States' or 'Behaviours' could be a Player characters Walking State, Running State, or the swinging of a Baseball Bat, Or could just be the Smoke of a Chimney.

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Sprites & Animations