Measurements are specified in mm, yes. How well they're adhered to depends on the application.
Factory-made kitchen cabinets, for example, are usually 600 mm wide, and this is pretty spot on (and since it's chipboard it won't warp much). The doors are specified a few mm under, so 597 mm for example.
Drywall comes in at 1200 mm; again, this is quite accurate. The studs then go on a convenient fraction, usually either 400 mm or 600 mm. However, there's much more leeway in precision since you don't see the studs once the wall is up.
And yes, seals and caulking and floor molding and other such tricks are used to cover up gaps where necessary.
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Personal anecdote: we recently got new a new fridge and a new freezer. I'd made measurements of the installation location (1200 mm), checked the appliance widths (595 mm), and figure it'd be tight but doable. Turns out the wall was slightly crooked, and I'd measured it near its widest location. Ended up cutting out the (chipboard) wall on one side.