Well a favor implies tit for tat, that you can ask a favor and by surrounding circumstances you’ll return the favor in kind. An example would be like at work between coworkers.

A gift, traditionally, is extended with no strings or caveats. Think a homeless beggar ( which I’ve experienced both sides of that scenario.

Favors could be said to be an exchange across time.

Gifts though culturally augmented to be included under the exchange umbrella are foundation-ally one sided