Their grate

Polyseme: Spelled the same, pronounced the same, same etymology

Homonym: Spelled the same, pronounced the same, different etymology

Homograph: Spelled the same, pronounced differently, regardless of etymology

Homophone: Spelled differently, pronounced the same, regardless of etymology

Polysemes are not homonyms, nor vice versa. Polyseme means “many meanings”, homonym means “same name”, homograph means “same writing”, homophone means “same sound”.

There is an alternate definition of homograph and homophone that is also legit that sees homograph as “spelled the same, regardless of pronounciation or etymology” and then vice versa for homophone. That definition is also legit, in which case a homograph can also be a polyseme or a homonym.

That doesn’t affect the relationship between homonyms and polysemes, although of course in the world of semantics, anything can happen.

The Answer