I'm not really savvy about harpoons. The larger ones mounted on whaler ships are definitely chemically-explosively propelled (like, you know, in guns), but whether there's smaller ones that use for example a spring or other mechanical device...well, I don't know. They'd be similar in that they store previously inserted mechanical energy to propel the projectile, but otherwise I've no idea.
A crossbow is essentially a semi automatic bow, where as a harpoon gun is a gun specially designed to shoot a harpoon.
Atleast I think so?
I hate to disagree, but no on the first part (the second one is obviously right). "Semi-Auto" basically means the entire mechanism sets itself up for the next shot after firing one. The closest we'd come to that is the Chinese repeating crossbows, but those were actually more like manual action weapons than semi-automatics (think pump-, bolt- or lever-action rifles/shotguns). What the crossbow is, is single-shot, like simpler modern anti-material rifles and grenade launchers often are. The bow cannot be compared to any manner of gun since it relies entirely on the user, and not on complex mechanisms.
Edit: Scratch the part about the Chinese Repeater being manual-action. It can't be fully compared, since manual-action guns still use explosive propellant instead of mechanical force for propelling the projectile. Only the reloading mechanisms can be compared.