is a specific kind of: do by, handle, treat.

is a broader term that covers: bait, cod, rag, rally, razz, ride, tantalise, tantalize, taunt, tease, twit | blackguard, guy, jest at, laugh at, make fun, poke fun, rib, ridicule, roast | deride.

derivation: jeer, jeering, mockery, scoff, scoffing | flouter, jeerer, mocker, scoffer.