You need to know that there are various 7mm's. They all shoot the same size bullet... .284 dia. There is a 7x57 Mauser, the 7mm Rem. Magnum, and the 7mm-08 to list the most common ones. I kind of assume you are asking about the differences between the 7mm Rem. Mag and the 7mm-08. The biggest difference between the two of them is the casing or shell that holds the powder and bullet. The 7mm Rem. Magnum is a much larger capacity case. It is called abelted magnum, due to the belt around the head of the case. It is primarily designed for larger game, such as elk, moose, medium sized bear etc. It is generally a more powerfuf round than the 7mm-08.
The 7mm-08 is basically a 308 Winchester case necked down from .30 caliber to .284 or 7mm caliber. The 7mm-08 has gained a huge following in recent years. It is a much more pleasant gun to shoot, generally shows good accuracy, and does a great job on deer-sized game. Not to say it has'nt been used with good success on black bear too, and I'm sure plenty of elk have been killed with it.
I have personally killed lots of deer with the 7mm Rem. Mag in years past, but have become a big fan of the 7mm-08 recently and it is now my go-to deer rifle.
I guess it depends on what you intend to hunt as to your choice. If you intend to reload for either, you have a fairly wide choice of bullet types and weights available You'll probably like the 7-08 better off the bench than it's big brother, due to the difference in recoil, with the 7 Mag being the heavier kicker of the two.
Hope this has answered most of your questions...........