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A lot of the terms are used interchangeably, but here is the definitions as I have know them:
A Sweeper is a produced short audio clip, often (but not always) used to brand the station, often used between songs or program elements. Think of the archetype laser sound effect and the big-announcer-voice booming “B-101 ROCKS” between two songs.
A Bumper is used to get into or out of a program block, such as the bumper music going into a network newscast when you have a few seconds to kill before the news begins, or the coming out of a local break, before rejoining a network feed. A bumper can be music, voice, sounds effects, or a combination.
A Stinger is a quick Sweeper with a kick. Sometimes used before or after a program element, or as part of a legal ID (when stations bother to do those).
Just my $.02 worth. Anyone feel free to add, expand or correct.