I am, or was for over 45 years, an amateur entomologist. Our daughter is now keeper of my "bug" collection.
Gleaned from several internet sites:
Cicadas are in the order Homoptera, most closely related to plant lice and leafhoppers.
Cicadas lay eggs in slits in twigs. Annual species hatch and mature on their host trees and sing loudly during hot summer days. Periodical cicadas drop to the ground after hatching and spend anywhere from a few to 17 years as nymphs feeding on tree roots underground before maturing to adults. Cicadas also destroy the small twigs on trees.
"Locust" is a general, colloquial term that usually refers to migratory grasshoppers of the order Orthoptera, but is sometimes applied to other insects of the order, including crickets, cicadas and katydids. Swarms of locusts were common during our Dust Bowl years, and there are still swarms of them throughout the world.