There's no easy answer to this, as the limits of "recreational" diving have changed over time. You definitely can't use breathing gas as the determining factor anymore.
"Technical diving" used to refer to any dive with a gas other than air. Therefore a 230 foot dive on air to the Andrea Doria wasn't a technical dive. Narced out of your skull crazy....but not technical. However, a 60 foot reef dive on nitrox was considered technical. This mostly stemmed from a long held belief in the mainstream diving community that blended gases were some sort of "voodoo." Well, through the persistence of a small group of advocates, nitrox is now ubiquitous among recreational divers and a light helium mixture, called triox, may soon be joining nitrox among the gases readily available to properly trained recreational divers.
To keep this simple, I will define a technical dive as one in which it is planned that a direct controlled emergency swimming ascent to the surface is impossible. This can occur either because you have placed a physical barrier between yourself and the surface (wreck, cavern or cave) or incur a staged decompression obligation.
"But wait," you say, "I've been inside wrecks on a recreational dive......and my computer has made me do deco stops after a few dives!"
Well, the operative word in my definition above is "planned." The primary difference between an idiotic recreational dive and a technical dive is planning. Just because you've pushed the limits of recreational diving out of arrogance or stupidity, doesn't make you a technical diver.
Coming soon: What does it take to be a technical diver?