Yes, the term "saturated" is trying to describe the hydrocarbon chain, even if it is functionalized with hetero- atoms (for example, O, N, and others.) If you have an unsaturated hydrocarbon, say a 15 carbon chain with one or more double bond carbons in it, if you put it under pressure with hydrogen gas and a catalyst, you can "saturate" the hydrocarbon -- replace the double bond in the carbons with single bonds to hydrogen. But, (AFAIK,) you can't use the same method turn a carboxylic acid into ... what, a hydrocarbon and two water molecules and half a hydrogen molecule? That just doesn't happen.