momus, moto-uno, you're confusing nominal roll film formats' (camera gate) sizes with actual. To begin with, the nominal metric sizes 6x6, 6x7, and 6x9 are sloppy approximations to the actual sizes. The nominal sizes in inches (2.25" x 3.25", 2.25" x 2.75", 2.25" x 3.25") are fairly close to actual. Actual sizes in metric are 56 mm x 56 mm, 56 mm x 68 - 70 mm and 56 mm x 78 mm - 82 mm (a few 6x9 roll holders have gates 84 mm long). There's some variation, usually slight, in gate length between makers.
Metric 6x8 doesn't have an equivalent in inches. Per a Fuji GX 680 II manual, the actual size is 56 x 76.
momus, 2x3 is an abbreviation of 2.25 x 3.25. 6x9 is, as I've said, a lousy metric approximation. These days both are primarily roll film formats, although b/w 2x3 (= 6x9) sheet film is still available. 6.5 x 9 is a metric sheet film format that doesn't, as far as I know, have an equivalent in inches.
People who don't all know this tie themselves in tight knots trying to make sense of it.