Does faster victory mean lower score?

Yes, at least indirectly.

Score is derived from a variety of factors, including number of cities, number of technologies, population, and wonders built. Many of these factors are things that you can and often will do more of if you are given more turns.

However, unlike some earlier Civ games, there is no score bonus for winning or ending the game early. This means that the longer you play without actually winning, the more chance you have to earn points and the higher your score will be.

If your goal is getting the highest score possible, you should subjugate your opponents, then spend as many turns as possible building an empire without winning.