P-metric sized tires are those with the "P" at the beginning of the tire size (such as P215/65R16). P-metric sizes were introduced in the United States in the mid 70s and are installed on vehicles primarily used to carry passengers including cars, station wagons, sport utility vehicles and even light duty pickup trucks. Their load capacity is based on an engineering formula which takes into account their physical size (the volume of space for air inside the tire) and the amount of air pressure (how tightly the air molecules are compressed). Since all P-metric sizes are all based on the formula for load, vehicle manufacturers can design their new vehicles (weights and wheelwell dimensions) around either existing or new tire sizes.
Metric or Euro metric sized tires are the ones without the "P" at the beginning, (such as 215/65R16). Using metric dimensions to reflect a tire's width actually began in Europe in the late 60s. However, since Euro metric sizes have been added over time based on the load and dimensional requirements of new vehicles, the tire manufacturers designed many new tire sizes and load capacities around the needs of new vehicles. Not quite as uniform as creating sizes using a formula, but they got the job done.
Euro metric and P-metric tires in the same size (i.e. P215/65R16 and 215/65R16) are equivalent in their dimensions with just slight differences in their load capacity calculations and inflation pressure tables.