Hunting
Bee species are a bit tamer in their food-gathering tactics when compared to wasps. Whereas bees search for nectar or pollen, most wasp species -- including those that live in the ground -- are hunters. They seek out insect prey, usually coming in the form of spiders.
Solitary
Wasps come in two varieties -- social and solitary. Social species are much more like bees, who live together in large social groups, collaborating together for the good of the colony. The solitary species -- including those wasp species that nest in the ground -- are independent and responsible for themselves and their offspring. Ground species are likely solitary because the nests are relatively small, not supporting a structure built for larger groups of wasps; the ground habitat may also be an evolutionary adaptation of previous solitary wasps (who lived in nests outside of the ground).
Stocking
When a female wasp maintains a nest in the ground, she'll stock it in preparation for laying eggs. Once a sufficient amount of food has been stocked, the wasp will lay eggs. Ground digging wasps differ on techniques, as some species will seal the hole, leaving the larvae to develop on their own. Others will leave the nest as-is and continually supply their young with food as they grow.
Example Species
One example of ground-nesting wasps is the Scoliid, which is dark blackish to purplish color, and also features a yellow stripe. The Tiphiid, which is unaggressive, looks similar to the Scoliid, with hairy, blackish bodies. Cicada Killers have a fierce name and a body to match, often growing up to two inches. They use their sting to capture prey, but they're relatively unaggressive toward humans.