The original was good, but it was the RADICALLY different cover version that was the hit

Cafe Society
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Ok, this one just crossed my mind. Back in the 1980s you may have heard some people talking about the steamy video for the Duran Duran song Girls on Film and wondered what the big deal was when on MTV you saw-

In truth that is the ‘Day’ version. The steamy video is in fact the NSFW ‘Night’ version.

It just so happens that I saw the ‘Night’ version first, when I was 14 or so. That ice cube was forever burned in my memory.
And it turns out the song is a different mix from the ‘Day’ version as well. I actually like the ‘Night’ mix better.

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To continue this little hijack, I remember Friday Night Videos breathlessly announcing they were going to be showing a video for a song that was banned by the BBC, implying that they had more guts than the Beeb. My first exposure to Frankie Goes To Hollywood was the so-called laser beam video for “Relax”.

Other than singing “come” a lot, I coudn’t figure out why it was banned. About a month later, the locally produced Goodnight LA (hands down the best music video program in history) showed the original golden showers video. … Oh, I get it now.

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A strong live action Tom of Finland vibe.

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More Shocking Blue

You may be more familiar with this version

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I am currenlty obssessed with the Ukelele Orchestra of Great Britain’s version of Psycho Killer. Worlds better than the Talking Heads original.

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Neither of these are hits, but they are radically different covers I like:
In light of the convo about Blue Monday -

And I don’t know if you can call it a cover if it’s just a reworking by the original songwriter: Mariachi Golden Brown:

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Since we seem to have drifted from the OP (a radically different cover version being the bigger hit) I’ll add a pair that interest me.

I love me some early Gary Numan (I linked to Are “Friends” Electric? earlier in this thread and here he is with Me, I disconnect From You which appeared on album but was never released as a single.

And here is the Grace Jones version which she recorded but never released until it emerged years later on an expanded re-issue version of her Nightclubbing album.

TCMF-2L