I just saw a nice photo web site that had galleries for "Animals", "Birds", and "Insects" and it reminded me of a pet peeve of mine. So that we always get it right here at BPN (and I'm sure we do!), the words Animal and Plant are levels of organism classification called Kingdoms. Within the Animal Kingdom are included groups of organisms such as insects, slugs, worms, birds, and of course mammals. It seems that it's quite common these days for lay people to consider mammals and animals as synonymous, which of course is incorrect.
Also reminds me of a perennial discussion I have in Antarctica after the first person says "Birds and Penguins".
My guess is that 'animal' is a colloquial term for species that have usually more than two legs, often fur and no wings (except bats). :) You are of course right that being more specific wouldn't be a bad idea.