Kanji are not words themselves (unless they are stand-alone in the Vocab section, like 女 does), but simply units of meaning. In English, we use words as units of meaning. As a result, we can use English words for many more situations than Japanese words can be used. In the case of “woman” and “girl:”
“That’s the problem with women.” Without context, you would use 女 here, because the speaker is referring to a trait pertaining to women in general. 人 means person, so tacking that on in 女の人 requires you be talking about a person rather than people as a whole. If the example sentence was pertaining to younger (college aged, for example) women and insinuating that the problem did not occur with mature women, 女子 could be used.
Essentially, the combined kanji usually “illustrate” the meaning:
女 is a standalone kanji, so it is the “overall” term for things female.
女子 is “woman” + “child.” It indicates the person is a woman, but is still child-like. This is why it refers to about the middle school to college age. They have enough maturity and physical development now to be distinguished as a woman, but they are still developing.
女の人 is pretty literal. It is a “woman” + person," indicating that a person is female.
少女 is “few” + “woman.” The person in question is female, but demonstrates few traits to show any maturity. This is used for young girls. 少女 is a bad term to use for an adult, as, like 乙女 Otome, it can technically assume “virgin.”
You’ll find a lot of synonyms as you progress through WaniKani, but analyzing the Kanji will be your best friend most of the time. Of course, there will always be those few that just don’t make sense. Jisho.org is pretty good about giving the context, so check it out if you’re ever confused.