The Cuttlebug (made by Provocraft) and the Big Shot and its family (made by Sizzix) do the same thing: use a manual cranking system to cut or emboss. The Cuttlebug is slightly smaller and more compact than the sturdier Big Shot.
The plates are individual to the machine, not interchangeable, but I'm guessing that you meant the embossing folders and dies. Nearly all dies and embossing folders from most manufacturers can be used in either machine.
So each does the same thing, and each machine has its own fan club. I'm a Cuttlebug girl, personally! I'm afraid I'm not helping you make a decision, am I?
Have a look at the product videos for each one, and some other machines that I've attached, and see if that helps?
Wow! Thanks Rosey for the information. Being new to this , it's a bit overwhelming. The videos did help alot, was able to get good visual of what they all do.
Thank you so much for your time, very much appreciated!