Fire engine, fire truck, fire brigade vehicle

I was subbing some copy recently that used the uncomfortable phrase "fire brigade vehicle". I changed this almost automatically to "fire engine" but then started wondering whether I'd done the right thing. Two issues were on my mind:

1. 'Fire engine' might be a totally or predominantly British English phrase. The Concise OED doesn't say so, although Googling 'fire engine' throws up a suspiciously high proportion of UK pages. I know that Americans might refer to a 'fire truck' but I don't know what the difference in usage is between 'fire truck' and 'fire engine' Stateside. 'Fire truck' doesn't appear in my Concise at all.

(Of course, the publication I work for is aimed at a British readership so really this isn't a big factor, but it's still interesting – and might explain why the writer shied away from using 'fire engine' in the first place.)

2. I don't know enough to say, but it could be that "fire brigade vehicle" is a more general term than "fire engine", covering vehicles other than those used to carry "firefighters and their equipment" (OED again). There was no way to tell from the story what type of vehicle was being referred to, so perhaps I should have played it safe.

My questions to you are: was I right to make the change? And what do you personally consider the difference is between 'fire engine', 'fire truck' and 'fire brigade vehicle'? Thanks!