One of the most common "old fashioned random variates" would yield a uniform distribution. Roll a six-sided die 6,000 times and you would expect 1,000 1's, 1,000 2's, 1,000 3's, etc, plus or minus some small variation due to chance.
Each possible outcome is equally viable, with the same percentage chance of occurring, and "ignores" the surrounding world.
Un-fuzzy logic (shaved logic?) says that "Given facts A, B, and C, the outcome shall be D".
Fuzzy logic attempts to capture some of the real world variability that is thought to exist in the process being modeled. Something like "Given facts A, B, and C, the outcome is likely to be a value drawn from this particular distribution named P.
Tweak either A, B, or C, and you may well be drawing distribution Q, or distribution R, etc, depending on the theory behind the fuzzy logic model.