Who's is a contraction. It means "who is."
Use who's in your writing only when you can substitute the words "who is."
Example of who's in a sentence.
Whose is a possessive pronoun, like my, his, her, their, and our.
It means "belonging to whom."
Use whose in your writing only when you mean to show ownership.
Examples of whose in sentences
Link to exercise on who's / whose.