EDG only deals with the number of domain numbers around the central atom.
2 domains = linear shape= sp
3 domains = trigonal planar shape = sp2
4 domains = tetrahedral shape = sp3
5 domains = trigonal bipyramidal shape = sp3d
6 domains = octahedral shape= sp3d2
MDG takes into account the #of bonds + the #of non-bonding e' pairs to make up the domain number.
2 domains = 2 bond + 0 nonbonding e' = linear shape = sp
3 domains = 3 bond + 0 nonbonding e' = trigonal planar shape = sp2
3 domains = 2 bond + 1 nonbonding e' pair = bent shape = sp2
4 domains = 4 bond + 0 nonbonding e' = tetrahedral shape = sp3
4 domains = 3 bond + 1 nonbonding e' pair = trigonal pyramidal shape = sp3
4 domains = 2 bond + 2 nonbonding e' pair = bent shape = sp3 (think water)
5 domains = 5 bond + 0 nonbonding e' pair = trigonal Bipyramidal = sp3d
5 domains = 4 bond + 1 nonbonding e' pair = seesaw = sp3d
5 domains = 3 bond + 2 nonbonding e' pair = T-shaped = sp3d
5 domains = 2 bond + 3 nonbonding e' pair = linear = sp3d
6 domains = 6 bond + 0 nonbonding e' pair = octahedral = sp3d2
6 domains = 5 bond + 1 nonbonding e' pair = square pyramidal = sp3d2
6 domains = 4 bond + 2 nonbonding e' pair = square pyramidal = sp3d2
After looking at this mess, I don't know if that helps explain or not. Really, the trick is to draw each shape and account for the bonds and nonbonded electron pairs. If you still have your Gen Chem book, I would think it is all laid out pretty well in the beginning chapters. Sorry if I added to your confusion. But one thing to recognize is that the names are the same for EDG and MDG if there are no nonbonded electron pairs.