Question About Roll System's

Hello I am trying to figure out the right wording so I can do some research on what is all out there, but I have no idea what its called. I believe DnD uses a D20 roll system as the type, but there are other things out there I've seen based on your skill determines the amount of dice you roll or the types or even exploding dice. If I recall correctly it was Shadowrun that makes you roll dice and a success is based on a 5 and 6. My issue is I have no idea what these are called, are these different roll systems or engine systems? What is the proper wording and if per chance does anyone have a link to a detail of a lot of them and pros and cons and maybe what is the most used as I honestly am not overly hyped on the DnD D20 system.