Is there a hierarchy to functional groups? I think I am getting slightly confused about the names we give to functional groups. I am aware that there are different types of functional groups such as alkyl, aryl and acyl groups. 

I also know that there exist functional groups such as those of esters, ketones and amides which come under the acyl group. However, thinking about this recently I also realised that there existed a carbonyl group, which is also present in a ketone?

I am also a bit confused as to whether the acyl group's general formula is RCO or RCOX where X could be a variety of groups. Also, is R a part of the functional group or is it there to show what the functional group is attached to. 

Could someone please make this hierarchy of functional groups a bit clearer?
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.