The type of tree that has round prickly seed pods is called a sweet gum tree.
It looks like the seed pods of Liquidamber styaciflua the Sweet Gum.
Coconut palm
The tree with long seed pods is the acacia tree.
The tree you are referring to is likely a sweetgum tree (Liquidambar styraciflua), which produces spiky round seed pods that are about 1 inch in diameter. These seed pods are commonly called "gumballs" or "spikey balls."
Horse chestnut is one.
The tree that produces brown seed pods is typically a mesquite tree.
The type of tree that produces long seed pods is called a "locust tree."
The type of tree that has long brown seed pods is commonly known as a mesquite tree.
The type of tree that produces long, flat seed pods is called a catalpa tree.
Trees that have hanging seed pods include the catalpa tree, the locust tree, and the Kentucky coffee tree.
A tree with round spiky balls might be a Sweetgum tree. See the Related Link below for a picture of the Sweetgum tree.
Oak tree seed pods are called Acorns.