"Never make a woman mad. Women can remember stuff that hasn't event happened yet."
Woman means an adult individual of the female gender. It is the singular term to characterize one adult Lady.
"I have always known Jane to be a kindhearted woman."
Women on the other hand represents more than one adult of the female gender. This naturally means two or more adult ladies, it is the plural term for 'woman'.
"Research shows that women deal with more stress than men."
Woman is singular. Women in plural. The spelling is no different from "man" and "men".