Regarding the tire size, let me further explain. You are correct about there being two "20 inch" sizes, one is 406 and the other is 451. You are also correct in that a 406 tire will not fit onto a 451 rim and vice versa. However, even if you have a 406 tire and a 406 rim, I don't believe that they are always compatible. Specifically, wide tires go with wide rims and narrow tires go with narrow rims. Here's an extreme example to illustrate my point:
http://www.sheldonbrown.com/harris/s...y-pugsley4.jpg
What you are looking at is Surly Bikes' "Pugsley", a mountain bike that takes 4 inch wide tires. And while the rims on the Pugsley are still 26 inch rims, just like on regular mountain bikes, they are much wider to accommodate the wide tires.
When you proposed putting Big Apples onto your Nova, I was concerned that the stock rims might not be wide enough to handle BA's 2 inch width, even though they are also the 406 size. Make sense?