Watch band compatibility of Apple Watch series 6 and series 10

There are 2 widths of strap

One fits all 38,40,41,42

The other fits all larger sizes

So yes, if you know if your Watches are both smaller or both larger cases

Yes, it will, see this: Older Apple Watch bands, including 41mm and 45mm sizes, will be compatible with the new 42mm and 46mm cases, and all new 42mm and 46mm bands will be compatible with older Apple Watch models.

Correct.