Is there a hierarchy to functional groups?
What you may be confusing is the difference between a functional group and a moiety. A moiety is a part of the molecule that could be either the whole functional group or just a part of the structure of a functional group.

Wikipedia does a decent job of explaining this.



In this illustration there is an ester functional group and an acetyl moeity.

As for your second question about the acyl group, my understanding is that the formula is RCO- and that the X is not necessary to define the acyl group. The R represents an alkyl group.