The first 4 types are s, p, d, and f. There are more however.
d orbitals have five positions.
4s 4p 4d 4f so 4 types
These numbers, when referenced in quantum mechanical electron orbital notation note the principle shell (or energy level) of the electrons specified. For example, 1s2 implies that there are two...
S orbital
s/sp2. p/p. sp/sp2. sp/sp.