I see your point. I think the issue is that the word "commute" has grown into many meanings. (these are my very simple off the head definitions but I think the point will be clear)

Commute (Verb), to move or travel

Commuter (Noun), one who travels to work

Commuter (Adjective-sort of) "I'm a bike commuter"

Commuter (Noun) a bicycle used for the act of commuting.

In other words...it's all symantics. My feeling is there are bikes that are made SPECIFIC to commuting. The ones that come with pre installed racks, fenders, etc. (yes, they might also be city bikes) OR bikes that have the set up for racks, fenders, etc. when you buy them.

HOWEVER...there are also all sorts of bikes that have been adapted to be bikes that commuters use hence also called commuter bikes. Maybe they should be called "Commuter's bikes"