The .44 Special is a little bit longer than the .44 Russian. The .44 Russian was introduced in the 1870s as a slightly more powerful version of the .44 American for Smith & Wesson's Russian-contract single-action breakdown revolver. The .44 Special was introduced later possibly as an evolution of the .44 Russian. (I can't put my hands on that citation at the moment, but I'm pretty certain I read it somwhere.) The information above on the .44 Russian comes from Philip B. Sharpe's Complete Guide to Handloading 3d Edition.
As for shooting a .44 Russian in a .44 Special/.44 Magnum revolver, I believe it should be okay, as they use the same diameter bullet, but I would prefer that someone else confirm that to you as well.