I think a "reef tank" is any aquarium primarily dedicated to maintaining corals and associated life.
The question gets tougher when you try to determine what level of success is required to fulfill the mandate. Some people throw a bunch of coral and fish in a freshly mixed box of water, all doomed. Is that a "reef tank"? If you change out all the dead stock daily your tank will have the appearance of a reef but the tenure of the inmates may be brief, still it technically qualifies. Just because a thing is done poorly doesn't change what sort of a thing it is.
While I personally enjoy studying the little things, the ugly bugs slimes and crusts as much as or perhaps more than oohing an awwing at the pretty colorful discs I can't say that my way is best or right. I like to limit the required human intervention and become an observer; a voyeur spying on the private lives of tropical sea-creature inmates going about their daily routine. If some prefer to continually have a hand-in(literally) maintaining natures balance who am I to draw the line? It's all cycles of life and death after all, the only variable is duration.
Edit: /begin rant
I'm glad so many people enjoy this hobby but I'm not sure I like where the hobby as a collective whole is headed. I frequently read ridiculously bad recommendations here such as "throw out all your liverock and start fresh" and my reaction is ***? someone with 5000 posts really thinks the appropriate move is to $hitcan a chunk of the ocean and buy the fresh? This in the same forum where it's taboo to keep a yellow tang in a 55! Morality is oh-so subjective. Reefkeeping has a whole industry now, like car tires or cigars. We have fans, advocates, shills and apologists they come along with the big money. Why should anyone feel passion for disposable commodities anyway?
In our visual stimulus overload centric culture a hopelessly overstocked coral smorgasboard is much more appealing than a sparsely populated yet environmentally stable box of rocks. Certainly the WWW is partially if not wholly to blame with it's instant gratification emphasis on pictoral/video content. In the heyday of rec.aquaria.reefs prior to AOL you only had internet access if you were a university student/faculty/staff or military/govt. The tight circle of reefing nerds weren't impressed so much by shiny things. In our global eternal September the slack jawed mouth breathers drive markets and media with their lust for shiny. That's why we have designer corals. That's why Acan frags are out of fashion and cheap just now. Style isn't predicated on reason, it has naught to do with biology, chemistry or physics and style is the master that compels seemingly rational, clever people to kill a box of exotic sea life out of plain ignorance and malaise just because it all looked so beautiful in the TOTM photos.
Even the nerds' devotion to technology has been perverted with a never ending product cycle of obscenely priced components that yield no measurable benefit over existing equipment in the hands of the average reefer. But hey, it's good for the economy if not for the reefs right?
/endrant