A mosquito inserts poison and a bee leaves half its body behind with a stinger attached to the poison. The bee loses a lot more than the sharp pain it gives. Unless you are allergic to bees. Than it can be life-threatening for both of you.
Mosquitoes inject a pain killer substance but you may feel the initial 'sting' as he pokes you. After a while, the 'pain killer' wears off and it itches.