A shallow league is one where there are not as many players per roster spot - eg. an AL only league where you cut out half of the players leaving a "shallow" player pool.
A deep league has a lot of players per manager either because there are few teams with few roster spots and because there is no restriction on who you can draft/purchase. This means that there is a "deep" player pool and nobody is starting Milton Bradley and Shawn Green's sorry ass is on the bench.
Cry your pardon, my man, but this is actually the opposite of how I usually hear these terms used. To wit: deep vs. shallow refers to how far into the available player pool the league has to go to fill its roster spots.
Fewer teams and/or fewer roster spots on each team means fewer players are on a roster at any particular time, and that league is shallow (i.e. doesn't go very far into the player pool) -- and good players are likely still on the waiver wire. In a deep league teams carry more players, and/or there are more teams so the pickings on the waiver wire are much less attractive.
Thus, in your examples above, a league where Milton Bradley and Shawn Green approach discard status is shallow; an AL or NL only league is neither deep nor shallow 'til we know how large rosters are.
Using Madison's average #'s above, an 8 team league with 22 roster spots/team would be shallow, especially in comparison to a 20 team/22 roster spot league where folks may even carry top-notch, potential minor-league call-ups.
By the way . . . been lurking all season. Thanks to all for the help and advice.