They are hemimetabolous, so a baby grasshopper looks like a miniature adult, only without wings. That's why the little ones can only hop away. If it flies from you, it's all grown up. Grasshoppers come in various sizes and shapes and are classified in the order Orthoptera, along with crickets and katydids.
'Short-horned' grasshoppers, belong to the family Acrididae. When many grasshoppers get together they are known as locusts.
These pictures are of the aptly named "Rainbow Grasshopper" Dactylotum bicolor. I found this one in Arizona during "The Bee Course" an excellent instructional course I took, which I'll have to detail in another post.
You can see the wing "buds". It probably only has one more molt to complete before it is an adult.
Grasshoppers have shorter antennae than the crickets and katydids
With full wings, this grasshopper can fly and is an adult.
Another large grasshopper nymph from Arizona.
This nymph blends in perfectly with the pink sand at Coral Pink Sand Dunes State Park, Utah.
The next two photos are of katydids. Katydids have long antennae like crickets and belong to the family Tettigoniidae. Also like crickets- they make sound by rubbing their wings together, while grasshoppers use their legs
This katydid is an adult female. You can see her curved blade-like ovipositor she uses to lay egss in tree branches.
A cricket nymph. Crickets belong to the family Gryllidae and usually have rounded heads and long antennae.
This black field cricket is eating a piece of dog food.
This is a Jerusalem cricket, which is despite the common name is not a true cricket. It belongs to the family Stenopelmatidae, large flightless insects. They are found in the western United States and Mexico and have many interesting common names such as the Navajo and Spanish names meaning 'skull insect' and 'earth child'.
They are nocturnal and live in burrows.