I went to the all-powerful internet for guidance (I mean, where else do you go). It seems like "female" denotes a larger biological category:
adjective:
female
- of or denoting the sex that can bear offspring or produce eggs, distinguished biologically by the production of gametes (ova) which can be fertilized by male gametes.
"a herd of female deer"
- relating to women or the female gender.
"a female name"
But included in that definition is "female" as woman.
Whereas "woman" means a female human being:
noun:
woman; plural noun: women
an adult female human being.
"a drawing of a young woman"
a female member of a workforce, team, etc.
"thousands of women were laid off"
a female person associated with a particular place, activity, or occupation.
"a Princeton woman was recently named the Young Lawyer of the Year"
It's a little confusing, but it makes sense. I guess being offended by it is another question. I have usually used the terms interchangably and have never been corrected or shamed for it. It seems like they are, for the most part, interchangeable.