There are predominantly two differing tyre types.
Radial and Bias - this describes the way in which the tyres internal cords are arranged during the manufacturing process
Bias -
The bias tyre is manufacrured by the ply cords being manufactured in layers & arranged at an angle. These layers are placed in a criss-cross pattern which means there is uniformity across the crown and the sidewall of the tyre.
Bias and Bias belted tyres are the two sub categories, traditionally the Bias belted tyres are usually a more robust construction..
Radial
Radial tyres are constructed from cords which have been rubber bonded and placed so they run across the circumference of the tyre. The radial piles are then covered by a casing belt made up of cord or steel which is then covered by the rubber tread.