Teem and team are not just homophones, they are also etymological kin. Teem comes from Old English tīman or tǣman, which originally meant "to bring forth offspring" or "to give birth to.” That word is related to the ancestor of team, the Old English noun tēam, meaning "offspring, lineage, or group of draft animals." Team can still be used to refer to a brood of young animals, especially pigs or ducks, but both teem and team have otherwise largely left their offspring-related senses behind.

What is the difference between the verbs teem and team?

If you want to describe an overflowing abundance of something, the word you are looking for is teem. We often see reference to "the teeming masses," "streets teeming with activity," or "forests teeming with life." You want the word team if you are trying to describe pairing two or more things in a coordinated ensemble ("she teamed the oxen together"), or forming some kind of partnership or association ("we are teaming with another organization this year").