I found a really simple summary online about some differences on truck tires:
DIAGONAL (BIAS-PLY) TIRES
These tires have body plies which cross at a substantial angle to the centerline of the tread and which strengthens both the sidewall and the tread area. Bias ply tires will almost always have an even number of body plies because using an odd number of plies causes a pull. Bias ply tires are usually constructed from nylon cord. Nylon has a wonderful property in that it shrinks when heated, but it also has an unfortunate tendency to take a set when statically loaded, especially when cold, resulting in a flat spot, the “square tire” syndrome. A flat spot will typically work itself out at the tires heat up after a few miles of driving.
A bias ply tire often won’t have much sidewall bulge, even at low inflation pressures.
At extremely low inflation pressures, a bias ply sidewall can wrinkle, similar to a drag racing slick.
Another common feature of bias ply tires is that the tread can wrap around and up the sidewall of the tire in an uninterrupted fashion. Since there is no transition from a circumferential belt to radial sidewall (the bias ply runs from bead to bead) this will not cause flex-induced heating.
The body cords run across the tire perpendicular to the beads. Radial tires have belt plies which run about 15° to the circumferential direction, under the tread, to stiffen, stabilize and strengthen the tread area. This results in less tread movement during contact with the road, so the belt plies improve tread life. Radial tires are usually constructed with polyester cords, which resist flat-spotting common in nylon cord.
A radial tire concentrated sidewall bulge at the tire contact point, even with proper inflation. It is difficult to determine if a radial tire is underinflated just by looking.
While some radial tires may have “tread” on the sidewall, it usually has a break at the sidewall transition and the sidewall tread is very thin to minimize heat buildup from radial sidewall flexing.
Either kind of tire can be constructed with additional belting under the tread, usually in the form of steel or aramid fibers for increased tread life and puncture resistance. The belts are always made of a bias ply material. In a radial tire, this causes a discontinuity where the sidewall and tread meet, thus the reason you never see radial tires with substantial sidewall tread. On a bias ply tire, the belting can help keep the tread face flatter to the road and since the tread and sidewall construction are the same, tread can be wrapped around and up the sidewalls for extra traction and protection.
The average steel-belted radial tire is made up of:
28% Carbon Black
27% Synthetic Rubber
14% Natural Rubber
10% Steel Wire
10% Extender Oil
4% Organic Fiber
4% Other Petroleum Products
3% (S, ZnO, Ti02, etc…)