Hi Charles,
No, and yes.
First, the no. For long-established names like Common Gull, Common Tern, etc, it tended to be selected for the species that is/was most conspicuous to the casual observer in England / Britain, regardless of whether they were the most widespread worldwide, nor even necessarily the most numerous in England
e.g. 1: Arctic Tern and Sandwich Tern are both more numerous than Common Tern in Britain, but are more concentrated in small areas so less visible to everyone as a whole
e.g. 2: Black-headed Gull is more numerous than Common Gull in Britain, but Common Gulls are more obvious to the average person because of their greater commensalism with man - the gulls that everyone sees on on urban school football pitches are mostly Commons, while the Black-headeds are mostly down on the south coast wetlands where nobody other than birders go.
After all, English names originally only applied in England, until later they also got used in other areas colonised by English-speaking people (USA, Australia, etc). Elsewhere, it would be the equivalent in the local lingo.
Second, the yes. A lot of birds are only represented in Britain by a single species, which had a single name, e.g. Raven, Cuckoo, Robin, Wren, etc. In recent years there has been a trend to invent qualifier terms to add to their names to distinguish them from other similar species (related or not!) with the same group name elsewhere in the world. In these cases, where 'Common' has been chosen as the qualifier (e.g. Common Raven, Common Cuckoo), there has been at least some attempt to select it only for species where it is the globally most widespread.
Michael