Both! वह and यह both mean he, she, and it. The difference is in the distance of the object. वह (usually pronounced vo) refers to something or someone that is far away or out of sight, and can also mean "that". यह (usually pronounced ye) refers to someone or something present or being pointed at, and also means "this". So the difference is NOT neither here nor there, the difference IS here and there ;) Hope that helps.
Ps, i am also a learner, so if any of that is wrong, please correct it :)
If I had to guess, it's probably because "She is a woman" sounds more natural than "That is a woman". Hindi ultimately doesn't distinguish between the two since pronouns are gender neutral, unlike in English, but in a majority of cases, when a Hindi speaker says, "वह एक औरत है।" a native English speaker would probably say "She is a woman."
The reason why "That's a woman" is incorrect is because the correct translation is "She's a woman" or "She is a woman" (I've tried both and both sentences are accepted).
The word वह can mean "that", "he", or "she" depending on context. When used to mean "he" or "she" there is an implication that the person being referred to is far away from the speaker similar to how "that" refers to an object away from the user.
Hindi's third person pronouns are gender neutral, unlike English which has distinct pronouns for male and female, but the pronouns do distinguish between distance. वह is for people or things that are away from the speak while यह is for objects or people near the speaker.