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The mm widths refer to exact rim diameter while the inch measurements refer to rim+tire diameter and are not exact.

This nails it. The nominal sizes are mostly (for some insane reason) based on the outside diameter of the wheel and tire. 27" road tires would have a 30mm tire size, whereas 27.5" mountain bike tires are probably running close to 60mm these days (haven't been keeping track of what's in vogue).

ETRTO is based on the bead seat diameter, which is what matters when you're buying a tire.

Not to forget: 29" wheels have the same rim diameter as 28" wheels used in road bikes (622mm). Obviously.

(The reason: mountain bikes use lager tires than road bikes, so the complete wheel is larger )

actual "27" is very old standard you might see such as if you discover an unused road bike from the early 1980s deep in somebody's garage. It's quite rare these days.

27.5 is used for mountain bikes so the rim profile and tire widths are a completely different thing than old "27"