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Slugger is an American colloquialism that means "a hard-hitting batter" (as in baseball) or someone who throws hard punches. Slug can mean "A piece of lead or other metal for firing from a gun; a roughly-formed bullet."
On the historical side of the question, the M36 carried one of the most powerful American anti-tank weapons (the 90mm M3).
So, that is why a big tank with a big gun was called a slugger.
All quotations from OED.
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British soldiers never gave it a name of anything. Why would they? They never used it.
"General Jackson" was the name assigned to the vehicle by Ordnance Branch in late 1944. US soldiers at the pointy end either never got the memo or, more likely, just didn't care.