Can a regular cake such as from a cake mix be baked in a springform pan? If so, will the results be the same as a normal cake pan?
"Regular" or springform pans is in my experience partly a cultural difference: In Germany you might have trouble to find a non-springform pan.
As long as the diameter is the same, you can freely substitute one for the other.
There is one exception, though: Most springform pans aren't watertight, so for a cheesecake in a water bath, you should either choose a regular pan (and face the trouble with unmolding) or see here for how to tighten them.