I've only played Original D&D, and 1st/2nd edition AD&D. Otherwise the RPG system I'm most familiar with is Fighting Fantasy. In my experience stats are rolled for, using whichever variant the DM prefers (some DMs are strict, while others allow more leeway). Some DMs use a home-brewed version that may involve adding traits from other game systems. In Fighting Fantasy, the basic variety of stats is simple: Strength (1d6+6), Stamina (2d6+12), and Luck (1d6+6). Depending on the specific adventure there may be other attributes, such as Fear and Honour.Standard 5e generation doesn't involve rolls, you take 15, 14, 13, 12, 10 and 8 and assign them as you wish.
Variant roll for assigning stats is to start with 27 points, and all your scores starting at 8. Number of points required for each score is as follows: 8, 0; 9, 1; 10, 2; 11, 3; 12, 4; 13, 5; 14, 7; 15, 9.
Variant roll for rolling is 4d6 with the lowest discarded, numbers assigned as you wish.