I was comparing the specs from my manual and saw that there is a higher lift in the 320 but everything else is the same. Does that mean the only difference is a different camshaft, the 240 having smaller lobes and the 320 having larger lobes? What else is different?

The main difference is the 320 has a longer stroke.

So if I were to get a different sized camshaft (one with higher lobes, maybe with new rocker arms and springs) it would produce the same horse power?

No. because the 320 is a larger engine and as the saying goes, "There is no replacement for displacement.