Lady or Duchess? What do these titles mean?

Answer 1

"Lady" isn't a noble title in and of itself, but rather the form of address for a noblewoman - that is, a woman who is a Duchess, or Countess, or any of a number of other titles would be referred to as "Lady Blah-Blah, Duchess of Whatever."

Duchess is the female form of a Duke, which has traditionally (particularly in the U.K.) been the highest non-royal (i.e., below Prince) title. In some smaller countries, the monarch might hold the title of Duke rather than King or Prince - though the only existing one is Luxembourg.