Typically there is a start (usually larger capacitance) and a run capacitor. Electrolytic capacitors are built with two foil strips (+ & -) with welded terminals which are separated by another 2 strips of electrolyte impregnated paper. This 4 layer strip is rolled into a cigar and put into the can. Electrolytic caps have a defined useful life. The ones that survive the early failure usually fail due to wear out mechanism. Most likely it is just the cap, if the motor runs as usual.

Imran Malik