There are two main types of Port; wood-aged and bottle-aged, with many sub-categories of each. To keep it simple the Port types have been broken down into their specific categories below. While most use the same type of grapes, the way in which they are selected, vinified, stored, and aged are very different.
Another way of thinking of the kinds of Port is White (made from white grapes), Ruby (made from red grapes, bottled fairly young, and intended either to be enjoyed young or aged in their bottle) and Tawny (made from red grapes but allowed to age in small wooden casks to accelerate the ageing and oxidation of the wine, which is ready to drink when bottled and not intended for bottle ageing, though some very fine wines may change character over time in bottle). There is also a unique style, Garrafeira Port, which is aged in both cask and glass demijohns.
See the FAQs about each specific type of Port:
Ruby Ports: Ruby, Reserve Ruby, Crusted, Single Quinta Vintage Port, Vintage Port
Tawny Ports: Colheita Port, Tawny Port, Tawny Port with Indication of Age