- Bees, Hornets, Waps, and Ant, are all members of the order Hymenoptera. Bees are considered a clade, called Anthophila. Hornets are a genus, called Vespa. Wasps are any members of the order Hymenoptera and suborder Apocrita that's not a Bee or an Ant. In other words, a Hornet is a Wasp. In some countries, "Wasp" refers to a kind of Wasp, the Yellowjacket. In Japanese, hachi ハチ refers to members of the Hymenoptera in general. There aren't terms that match Wasp and Hornet, although suzumebachi 雀蜂 may refer to the subfamily Vespinae, which includes Hornets and some Wasps.
Beware: some kanji that are difficult to handwrite are easy to type on the computer, which may skew the usage statistics.