A priest is ordained and can perform the holy sacraments like communion and baptism. A priest lives within a community and serves them as a spiritual guide and to perform the necessary sacraments for them. Go into a chapel and the guy doing things in there like taking confession? That is a priest.

A monk has taken vows and frequently joined an order. Vows of obedience within an order are common among the vows monks take. Other common vows would be to poverty, service, silence, and the like. Generally the idea of being a monk is to separate oneself from the general population to approach God. So one would leave town go to an isolated location to join a small group of individuals with whom you would not interact much. There you would seek God in solitude.

One can be both a priest and a monk. But most monks would not be priests.

Both the Eastern and Western churches had priests and monks. The Eastern was more likely to have truly isolated monks living complete isolation. But both had/have priests. And both had/have formal orders of monks.