Stick insects belong to the family of Phasmatidae, while leaf
insects belong to Phylliidae.
Both are from the order of Phasmatodea, and are therefore easily
confused. For example, Extatosoma Tiaratum is commonly known by the
name 'Spiny Leaf Stick Insect'. Having 'Leaf' in the name can
confuse it with the family Phylliidae, though it's actually a
Phasmid. For this reason, when researching, and writing reports,
it's important to be certain of which family an insect belongs
to.
If you want a simple answer, stick insects tend to look more
like sticks, and leaf insects like leaves, though again, they can
be easily confused.