Whose
Whose is the possessive form of
who. It means 'belonging to whom'.
Whose usually sits before a
noun.

Conscience is a mother-in-law whose visit never ends.

("Whose" sits before the noun "visit". "Whose" in this example is a
relative pronoun.)

Whose bike was expensive?

("Whose" sits before the noun "bike". "Whose" in this example is an
interrogative pronoun.)

Carl knows the girl whose phone was stolen.

("Whose" sits before the noun "phone". "Whose" in this example is a
relative pronoun.)
Who's
Who's is a
contraction of either
who is or
who has. It has no other uses.

Who's coming to fix the bed?

(who is)

Who's eaten the last muffin?

(who has)

I met the inspector who's delivering tomorrow's briefing.

(who's)