The words male and female are used as classifications (such as in anthropology, or medicine), and they can be used as adjectives as readily as nouns. The words man and woman are more personal descriptors of individuals.

When using these words to describe the subjects of a scientific study, we might find either of these:

•The control group consisted of 26 female and 18 male patients.
•The control group consisted of 26 women and 18 men.

You are right about how your second example sentence sounds "off", but that's because you've mixed the two words:

•The woman pointed the gun at the man. (sounds normal)
•The female pointed the gun at the man. (sounds awkward)
•The woman pointed the gun at the male. (also sounds awkward)
•The female pointed the gun at the male. (sounds acceptable)

However, context could very well override that general guidance. Some of the sentences I've labeled as awkward may sound funny on their own, but they could be just fine in the middle of a lengthy testimony during a courtroom trial, where a long series of questions has set up a scene - i.e., something like this:

"What did you see in the room?"
"There was a woman with a gun, and two people in the doorway."
"Could you tell if those two people were male or female?"
"Yes."
"And what did you notice?"
"There was one male, and one female."
"And what happened next?"
"The woman pointed the gun at the female."

I think that last sentence reads just fine in that context, because the preceding dialog has made it rather easy to follow along.

Female and male are useful in cases where it is not clear, or the speaker doesn’t want to say, whether or not the person referred to is a juvenile. You will sometimes find them used in, for example, police reports. However, where the age of the person is known, it’s preferable to use the relevant term, such as woman, girl or young woman, or man, boy, lad or young man.

When it comes to describing professions, questions of equality influence the language we use. It is advisable to refer to a doctor simply as a doctor. You can always say whether the doctor is a man or a woman later in the conversation if the need arises.

Female is a word only defining the gender.
On the other hand, woman means a female who is also an adult.

Usage

Female is rarely used, and usually used only in formal written English.
Woman is used quite commonly, as illustrated by your example.
If the person concerned is not an adult but a female, people usually use girl or young woman.

Same for 'man' and 'male'.

A very similar thing happens in Japanese. The Japanese word for woman is onna, corresponding to the character 女. But if you simply call someone onna (for instance ano onna ...: that woman ...) it is abrupt, and offensive to that woman and the person you're talking to. People do not say this. The word used is onna-no hito (女の人), at the very least, or other words like josei　（女性）. However, in news reports, the word onna will often be used by itself to refer to a criminal suspect. It is not rude in that situation, but rather it is analogous to when English-speaking police or reporters say female suspect. "According to the security camera footage, the female suspect entered the building at 15:03 ..." "The suspect is described a female between 35 and 40, five foot three, wearing ..." "There were two perpetrators, a male and a female. The male was armed with a semi-automatic weapon ..." But it would be strange to use female to refer to a woman in everyday speech. The following are inappropriate and weird. My boss is a nice female. There is a female at the front desk, asking for Mr. Jones.

So that is the essence of female versus woman, when female is used to refer to a woman: the speaker is placing some kind of mental distance between him or herself and the subject, and not identifying with the woman as a fellow person.