As to where these cuff styles came from, the gauntlet cuff probably originated from the common round cuffs of 18th century jackets. These were originally fully functional (they could be unbuttoned to lengthen the sleeve for cold weather).
Now just why Highland cuffs and Highland spats later aquired points at the back, who can say.
The slash cuff was also originally functional, as can be seen here:
There was a time when both cuff styles were used concurrently in the military:
The doublets adopted by Scottish regiments in 1855 originally had slash cuffs:
But later the cuffs were switched to the gauntlet style:
In any case they're common with civilian kilt jackets nowadays. Here you'll see all three styles:
What's interesting (to myself anyhow) is that there was in the mid 19th century yet another cuff style, which came to a point in the middle, which for whatever reason isn't often seen nowadays. Here it is, on the brown tweed day jacket, and on the tartan jacket worn by the stout gent:
It's still to be seen in the wonderfully "retro" uniforms of The Atholl Highlanders:
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