Yes, you can shoot 44Spec. in your 44mag. But, no, you can not shoot 44magnum in a
gun chambered for 44spec. Both cartridges use bullets of .429" diameter. The difference is in the case length, the magnum being a little bit longer, and of course the
magnum is loaded to higher pressures. 44Spec. shouldn't be too hard to find. I think
all the majors make a factory load for it. Readily available via the Internet also. Here's some links for ammo:

CheaperThanDirt: http://www.cheaperthandirt.com/ctd/default.asp

AmmoMan: http://www.ammoman.com/default.htm