a messenger: someone sent by another to carry a message or do an errand on the sender's behalf, whether a human envoy or a heavenly being (an angel).
At its heart this is a job word, not a description of what someone is made of. It names anyone who is sent to speak or act for the one who sent them. The same word covers a king's envoy walking the road to a foreign court and a heavenly being standing in God's presence, because both are doing the same thing: carrying word and authority that are not their own. This is why English splits it into two words, messenger and angel, while Hebrew uses one.
What changes from place to place is simply who does the sending. When a person or king sends, the messenger is a human envoy. When God sends, the messenger is a heavenly being, what English calls an angel. The figure can also be a prophet or priest, a human being God has sent with his word. Because the messenger speaks for the sender, the message often comes out as if the sender were present, which is part of why heavenly messengers in these stories can be so easily mistaken for God himself.
One use stands apart and has drawn centuries of discussion: the angel of the LORD. In several scenes this figure speaks as God, is addressed as God, and is treated as God, yet is also spoken of as distinct from him. Readers have long disagreed over whether this is simply one of God's heavenly messengers, a way of describing God making himself visible, or something more. The word itself does not settle the question; it only tells us this is one sent by God.