It's prudent to use water bottle cages that will adapt to bottle diameters within some range, to allow using multiple bottles in the same cage.
Naturally, this flexibility is to be hedged against safety. If the bottle needs to be squeezed in or out, that just distracts from the road.
In any case, I ordered a water bottle cage that turned out to have a fixed diameter of about 2 3/4", or about 70mm. A smaller bottle will rattle, and the full circle enclosure won't allow anything bigger.
A fixed size might be a good thing. If there exists some international / conventional size for bike water bottles, then a perfect fit will ensure that pulling a bottle and returning it can be done effortlessly (and hence safely).
Does such a conventional diameter exist?
I'm rather partial to metal containers glazed with ceramic, since these guarantee they won't react with the water, but since these seem to be available only in carabiner format that's not suitable for cycling, I'll have to settle for plastic bottles.
Update (following Carel's answer)
After two searches it's clear which brand Carel means. A big advantage is that those bottles are indeed listed as having ⌀ of 71, and so perhaps there does exist some convention at that diameter.
There are also stainless steel bottles from other makers, which should be perfectly safe, as well as ecological since they would last forever (unless/until lost).
Update (following Vladimir F's answer)
It's nice that the standard size is quoted in a wikipedia article (though without references). I wish the manufacturers were notified of the existence of this convention. Cycling aside, it would be nice if knapsack makers also followed the same convention.
As for getting a bottle-cage pair as one product, I'm not crazy about getting bottles and holders from the same maker, because I would have a hard time deciding what's better, to get a bottle from a bike maker or to get a cage from a bottle maker.