In all honesty, I never really paid much attention in biology class. Well, not enough to retain anything useful, anway. I'm guessing that's because they probably weren't delivering any scintilating lectures on the distinction between a whale and a dolphin (something I would have been interested to know). Sigh. Public education never did cater much to my personal interests.
But that's what Wikipedia is for. Right? 
For the purpose of this lecture, let's assume they know what they're talking about.
In college, one of my many roommates was an Italian vet student who, to the best of my ability to understand her broken English, was interning at the A&M marine center. I would have LOVED to be able to talk with her about her studies and her experiences with dolphins but the language barrier was just too great and, instead, we mostly ended up getting in each others way and on each other's nerves. Sad.
Anyway. She had one of her text books open one day and I was startled to realize, as I was looking at it, that Orcas are "part of" the dolphin family. For whatever reason I didn't pursue that line of curiosity any further at the time. But it occurred to me to do it just now.
I have always been drawn to the sweet and beautiful bottlenosed dolphin. I am captivated by their grace, their agility and the idea that their intelligence might rival our own, if perhaps in some unknowable way. In those science classes in school, it always seemed as though Dolphins were just being lumped together with all the other sea mammals, as though there were no special distinction between them. And maybe there isn't, really. Maybe one is no more intelligent or interesting than the other. Maybe the bottlenose dolphin is just cuter and, therefore, a better crowd pleaser than, say, a hump back whale.
What can I say? I'm a sucker for the cute ones. I have to believe, though, that there is some greater life energy to these beings who leap for joy with such enthusiasm.
Anyway, the questions at hand when I got started this evening, were these: Are dolphins "whales"? and Are Orcas dolphins?
The somewhat complex answer is this.
The Cetacean order (within the Mammal class) consists of whales, dolphins and porpoises. "Dolphin" is a generic term used to describe both Oceanic (Delfinidae) and River (Platanistoidea) dolphins. Both families of dolphin (as well as some whales) are subordered as "toothed whales" because they have teeth. Within the Delfinidae family are more than a dozen genera which include bottlenosed dolphins, other oceanic dolphins, several sea animals that have been incorrectly referred to as "whales", and the beautiful and enormous Orca (aka Killer Whale).
In summary: Dolphins are part of the same order and (in some cases) suborder as whales. And Orcas are dolphins (when "dolphin" is defined as a member of the Delfinidae family).
I love those sweet little dolphies! 
If I can find a cool design, they are sooo next up on my tattoo wish list!