What threading type is my ice maker shut off valve?
One side of your needle valve is 1/4" compression thread, that is the side with tubing connected to it. The watertight connection is accomplished when the compression nut squeezes down upon and cinches the compression ferrule (a brass sleeve that fits over the tubing) tightly to the tubing.

The other end is 1/8" NPT (National Pipe Thread). NPT fittings seal by the taper of the thread (with teflon tape or pipe thread compound to facilitate) and are utterly incompatible with other types of threaded fittings. 

You will likely need an adapter to fasten the valve to "the male end... on the back of the fridge". If you post a picture of that end we might be able to tell you the type of adapter you need.