Knock knock. Who's there? It's an apostrophe telling you that who's is short for "who is." Whose silly idea was it to make these words sound alike? Who knows? But whose shows possession and who's is a contraction.
Who's confused? Not you! With an apostrophe, who's is always short for "who is" or "who has." Sure, apostrophes show possession, but they also replace letters in a contraction, especially with pronouns like "who" and "it." The apostrophe indicates the missing letter. When an apostrophe is used with a pronoun, it's (see there?) often a contraction, like the examples from these fairy tales:
"Who's Afraid of the Big Bad Wolf?" (Three Little Pigs)
"Who's been eating my porridge?" (Goldilocks and the Three Little Bears)
But whose is like "his" or "hers." It shows possession without an apostrophe because it's already a possessive pronoun. Possessive pronouns don't need no stinking apostrophes! Whose is the possessive form of "who" and "which." So, whose can refer back to ideas, where "of which" doesn't fit, as in "a question whose answer is required." Pretty stuffy. Here are better examples:
"Nothing is more powerful than an idea whose time has come." (Victor Hugo)
"Whose Line Is It Anyway?" (TV show)
If you forget, remember that who's is often a question — it has a little space waiting for an answer. That apostrophe stands for "is." Whose owns it all. It's possessive, like a kid who keeps all the toys close. The bottom line is that who's is short for "who is," and whose shows ownership.