Hi, I am a year long reader on this board. I have been needing to sign up, so this question was my excuse. Hi everyone!
The 44 Special is to the 44 Magnum much like the 38 Special is to the 357 Magnum. In these cases the "Specials" came around first. As metallurgy and powders improved, firearms of the same chambering were able to handle more powerful loads. In order to keep these loads from damaging weaker older guns the cases were lengthened so as to fit only new makes of proper safety margins. There is slightly more to it than this but this is it in a nutshell.
The 44 Special was used by a legend in the firearms world. This man was Elmer Keith (Google his name and do some reading, it is worth it!). He hot loaded the 44 special and did amazing things with it. He is responsible for us having the 44 Magnum.
For you as a Marlin 1894 owner it means that you can safely shot Specials in your firearm when you want less noise, power, and recoil. These are really nice so you can distinguish which rounds you might use for a given purpose. You might use 44 Magnum rounds for hunting and 44 Specials for "fun" shooting at cans, targets, and small game hunting. 44 Specials also are great training rounds as you don't have the load blast and sharp recoil with these.
If you shot lots of Specials be sure to scrub your chamber to remove any fowling before using Magnums, as you can experience feed problems with the longer magnums otherwise.