Hi Emily!
Great question. You're right! Ether, like alcohol, is both a functional group and a shorthand name for one of its family members. So, ether can refer to EITHER the functional group of R-O-R or the specific molecule dimethyl ether. You have to figure out based on context. Just like alcohol can refer to either the functional group -OH or the molecule ethanol.
If you see "ether" under a reaction arrow, it is likely referring to dimethyl ether as the solvent.
The R-O bond is weakly polar, and becomes LESS polar as the R-chain gets longer. Ethers are more polar than alkanes, but less polar than alcohols and ketones.
Dimethyl ether has the same "polarity" as benzene, and should be considered non-polar and aprotic.