Can I use a lens that normally should be used on a DSLR, but mount it on a SLT? If not, what is the difference between a DSLR lens and a SLT lens?
My camera is a Sony α68.
Yes. Sony A-mount lenses (and Minolta A-mount lenses) can be mounted on your camera.
From the standpoint of the lens operation (focusing motor, aperture, mount, etc.), there is no difference between a SLR with a mirror and a SLT with a pellicle mirror. Lenses for your Sony Alpha 68 use the A-mount system, just like any other Sony interchangeable lens camera with a mirror.
It is possible in some cases to mount lenses from other manufacturers on the Sony A-mount bodies. This usually results in reduced functionality (usually loss of autofocus, and perhaps aperture control). Lenses for most camera systems with a larger flange focus distance or registration distance than the A-mount (44.5mm) can be physically mounted on the Sony body by use of an appropriate adapter.