What is the difference between polar capacitors and bipolar capacitors?

Polar capacitors are acidic wet dielectric type capacitors which work only when there is a DC voltage present between its two leads in right polarity. Polar capacitors are ideally suited for a DC power supply ripple filter. When connected in wrong polarity, chemical reactions within a polar capacitor can cause them to blow up, often violently, causing injury to someone nearby. Most polar capacitors these days come with a safety valve to release internal pressure build up.

Non polar capacitors are usually dry types made of ceramic, mylar, polyester or any possible dry insulator as a dielectric. Two polar capacitors connected back to back also make a non-polar capacitor. They work well in all situations whether there is any DC voltage present between their leads or not. Non polar capacitors are often very large and impractical in most applications except where a small capacitance value is required.

Some good applications for non-polar capacitors are: an AC motor starter, an AC line spike filter and a crossover network. Since voltages across an AC motor or inside a speaker system consist only of pure AC, polar capacitors cannot be used in those cases.

Polarized capacitors are typically large devices known as electrolytic or tantalum type packages, used for filtering or stabilizing voltage sources, usually in DC type circuits. Construction of these is if I recall correctly, an aluminum foil called the anode (positive lead), separated by an oxide film with a dielectric material known as the cathode (negative lead), hence polarity.

Non-polarized are similar to polarized except the plates are similar metal.

Polarized caps are typically used in large voltage situations, such as DC line filtering to reduce noise related to uneven voltage levels after rectification from an AC source. Mainly measured in microfarads. Polarity is critical to these devices. They are marked with the voltage rating (usually double the circuit voltage used) as well as the farad marking.

non-polarized caps are typically used in low voltage situations, both AC and DC. Polarity is not critical. Measured in pico farads typically.