In a 12gage a full choke has about .030" constriction (choke). A modified choke or also called a 1/2 choke has .015". the 12gauge has a nominal bore of about .728", but some back bored barrels are as much as .740 or even bigger.
A 20 gauge on the other hand is smaller with a bore of .625" to .630 with .025" choke for full choke and about .012" for modified. there don't seams to be any real standard for chokes and bores each maker has their own ideas of what choke is what.
12and 20 bore or gauge means there are 12 or 20 round lead balls to a pound of lead. The 410 is the actual bore diameter in inches .410".
Buck shot is not well suited to the 20 gauge, because it will not hold too many lead .30 cal. pellets. A 12 gauge has more room in the case for more buck shot balls. A 3" 12g is even better for buck shot.
Both 12 and 20 will shoot slugs, 12g with a 1 oz slug, 20g with a 3/4oz slug both quite good for deer at close woods ranges.