Dolphins and whales are similar in many ways; they are alike in the sense that both are marine mammals and they both belong to the order of cetacean.
The order Cetacean includes whales, dolphins, and porpoises.
While all cetaceans are mammals fully adapted to the marine life, they split into two suborders, Mysticeti which includes the baleen whales and the Odontoceti which includes all the toothed whales, dolphins and porpoises.
Whales and dolphins, share several characteristics like the need to breathe fresh air, which they do through blowholes in the top of their head, but whales have two of them while dolphins have only one.
Also, they both are mammals, so they nurse their kids with milk from the mother and provide maternal care for years until the calves are big enough to defend themselves from predators.
However, the most noticeable different between baleen whales and dolphins is the way they feed, while Mysticeti feeds on krill and plankton, Odontoceti feeds on fish and squid mainly.
There are six species of dolphins that are called whales because of their size, characteristics or similar look, but they are not whales.
Melon-headed Whale, Peponocephala electra
Killer whale (Orca), Orcinus orca
Pygmy Killer Whale, Feresa attenuata
False Killer Whale, Pseudorca crassidens
Long-finned Pilot Whale, Globicephala melas
Short-finned Pilot Whale, Globicephala macrorhynchus
It is important not confuse whales from dolphins although dolphins are an informal group inside the order Cetacea. They are not part of the taxonomic order.