A porpoise is a porpoise. It's not a fish and it's not a dolphin. They are warm-blooded mammals that breathe air using lungs and the young suckle milk from their mothers. A porpoise is actually a dolphin's cousin. Similar but still two worlds a part like any extended family.
Porpoises belong to the Family Phocoenidae, not Delphinidae like the dolphin does. They both are cetaceans along with whales. Unlike dolphins who live by the equator, porpoises live all over in the northern hemisphere.
Porpoises, unlike dolphins, don't have extended snouts or beaks, big bulbous foreheads or large flippers. Their dorsal fins are smaller and triangular, their teeth are a spade-shaped and their flutes are notched. While dolphins love to bow-ride and perform acrobatic leaps out of the water, also known as breaching, porpoises rarely do.
The common porpoise resembles a dolphin but makes a distinct puffing sound when they breathe. This is often the only way to locate one in the vicinity. Like most species of porpoises, they are timid and wary of boats. Making this water-bound mammal rarely observed in the wild. While the Dall's porpoise looks a lot like a killer whale, it's the fastest of all the small cetaceans. It can reach speeds of 30 knots, a wake is created known as a rooster tail, this allows the Dall's porpoise a hollow area for breathing air, keeping the body slightly submerged under the water's surface.
Within the Phocoenidae family, there are six species of porpoises; Harbor Porpoise, Dall's Porpoise, Spectacled Porpoise, Burmeister's Porpoise, Finless Porpoise and finally Vaquita.
http://www.acsonline.org/factpack/HarborPorpoise.htm
http://www.theporpoisepage.com/