Probably a Stupid Question: Ethereum vs Ether

I understand the differences between Ethereum and Ether. The former is the blockchain network where programs can be built on top and the latter is the native cryptocurrency that is used as an incentive for nodes to keep the system running and validated.

My question is this: on exchanges, such as Coinbase, the commodity one can own is labeled "Ethereum," which doesn't make sense to me as Ethereum is a network, and therefore, doesn't have a pin-pointed value. Does one actually own Ether and is it perhaps just mislabeled or am I just really not understanding how these commodities work?