Dremel bits are Not effective for use in a Power Drill. The rotary tool requires a high RPM to cut, carve, or etch, which power drills do not provide.
A rotary tool provides high speed but not the "torque" produced by drills for drilling through wood, concrete, or driving screws.
Because Dremel bits won't function properly in a drill, regular drill or driver bits will not fit into a Dremel or rotary tool. As I said, that's the longer answer :)