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Difference between TMJ and FMJ is in manufacturing process.
TMJ bullet is a cast lead bullet with a thin copper plating all around. It's not actually a "jacket"
FMJ's are made by first drawing the jacket, and then pressing lead core into it. FMJ bullet can have exposed lead at either base OR tip (depending from which side the core was pressed in). Some FMJ bullets have the opening capped off, and therefore don't have any exposed lead.
Main reason for using TMJ's over FMJ is cost.
"...OR tip..." That'd be a Soft Point.
"...STHP - Soft Tip Hollow Point..." Nope. Silvertip Hollow Point.
A 'net search for 'bullet abbreviations' turns up 1.33 million sites on Google. None of which are complete either. The manufacturers will have a different name for the same thing too. Be easier for you to just ask here.