A click - or track - has become the term used to describe something that regulates a performance, but a metronome provides tempo for practice purposes (or in non-conducted recordings, a metronome would be recorded on a spare track, and it became the consistent click for the rhythm as well as overdubs.)
Hard to say for sure when clicks crept into recordings or performances. They were used for radio and tv ads to regulate their length in the '60s (and probably earlier than that via the use of a metronome and conductor, when there weren't spare tracks for the click.)
The first songs I recall that obviously used a click, both from 1971, were:
1) "Family Affair" by Sly & the Family Stone. It's a rhythm box that runs through the song, with live drums. It was obviously used for its retro but cool sound, and not to regulate tempo, or it wouldn't have appeared in the mix.
2) "Baba O'Riley" by the Who would also qualify, with the synth acting both as a melodic element, and tempo regulator for Keith (which I'm sure he loved!) But they may have been the first to use it live - the recorded synth part was also used in concert, and acted as a click (or more accurately, a track.)
But five years prior in 1966, the Beatles used a drum loop - 1 bar of Ringo's playing - in "Tomorrow Never Knows", which in effect, acted as both a click, and the drum part.
Seems like this was discussed before, and I don't remember if we ever got to the bottom of it. But by the late '70s, using clicks for tempo was more prevalent in studios, and today, I'd venture to say that 99% or recordings are made with a digital click of some sort. Hard to say what percentage of artists use it live, but I think 50% is a safe guess.
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