There are 3 basic designs. In chronological order, the first is the tri-cone, which had 3 small cones with a T-shaped bridge support attached to the centers of the cones (these were all metal bodied, and have been reissued the last few years, as the necessary tooling became affordable in Asian countries). Next came the National biscuit bridge, which has a single resonator about 9-1/2" diameter sitting in a hole in the middle of the top, with its edges rested on the rim of the hole (these were all metal originally, because the guys who developed it were basically metal workers and didn't have the woodworking chops for bending sides, etc). "Biscuit bridge" derives from the fact that the bridge is mounted on a round "biscuit" that sits in the center of the resonator. The third one is the Dobro spider bridge, where the 10-1/2" resonator sits on top of a round "soundwell" of laminated maple that extends from the top to the back. The bridge is mounted on a "spider", the legs of which rest on the lip of the resonator. These have been made in metal and wood, and later, when Dobro and National joined forces, wood-bodied Nationals became available.
I haven't played
a tricone, but I have played many Dobros and biscuit bridges, and I own a wood-body Dobro and an Epiphone Biscuit.
A good biscuit bridge sounds almost like an electric, with a strong midrange. It won't sustain as well as a spider bridge, but it is excellent for blues. A bad biscuit bridge sounds like a banjo, so it's important to try them before you buy.
A spider bridge is sweeter, with good sustain, and a twangy tone. Another one that you have to try first, because a bad sounding spider bridge is useless: trebly, thin and rattly.
One thing about resonators: don't string 'em with slinkies! They need fat strings to come to life. Those resonators need some punch driving them. A set of Dobro strings runs .056W-.016, low to high. I put a set of acoustic mediums (.056W-.013) on my Epi, and as soon as I change strings I'm going to the Dobro set.