According to Naver's English-Korean dictionary, it can mean both the physical plate, as well as the food on the plate, but I have no idea if one meaning is used more often than another (I'm a Korean beginner). https://en.dict.naver.com/#/entry/koen/3629ae0fc8024eb4b782e645ccea990b
what deos it mean to receive a plate from a man?
man: (sees an attractive woman on her own in a restaurant and asks the waiter) could you send tokujo nigiri set to table A?
waiter :(to the woman) madam, this is for you from the gentleman at table B.
woman: (looks at the man in surprise)
man: (smiles at her creepily)
에 and 에서 are used with inanimate beings. To the tree: 나무에; from the rock: 돌에서; in a museum: 박물관에(서). In other words, we use these two (에 and 에서) with objects and places.
But for people and animals, we use 에게 and 에게서 instead. For example:
선생님에게 묻다 - to ask a teacher (literally "to ask to a teacher") 남자에게서 선물을 받다 - to receive a present from a man.