If that’s a wasp and a yellow-jacket is a wasp, then so are ants and bees,

That logic doesn’t check out, given Sapygidae is a family of sapygid wasps belonging to the Aculeata infraorder.

Aculeata is named after its defining feature, which is the modification of the ovipositor into a stinger. This trait doesn’t strictly constitute a wasp, which is why they have their own families (Vespidae, Sapygidae, Pompilidae, Myrmosidae, basically all of the Chrysidoidea superfamily, etc.).

All wasps are aculeate, but not all aculeates are wasps.