Would the word "lady" be a proper term for a woman as the word "gentleman" might be for a man? Is there even any distinction between the two or does it not matter at all really?

I thought up this question while driving to work today. I know it isn’t of any earth shattering significance but I was just wondering what kind of usages people prefer.

(I know I could have consulted a dictionary on this but I prefer the thoughts and opinions of Flutherites as opposed to what I could have learned from dry, impersonal reference materials.)