The key difference between ethanol and dimethyl ether is that the ethanol is a colorless liquid at room temperature which has high volatility whereas dimethyl ether is a colorless gas at room temperature. Further ethanol (common name is ethyl alcohol) is an alcohol while dimethyl ether is an ether.
An alcohol is an organic compound composed of a hydroxyl group (-OH) as the functional group. An ether is also an organic compound, but it has two alkyl groups attached to the same oxygen atom.