While you are not completely wrong, boxmaker, you are FAR from accurate... Capacitors ARE rated in farads, (named after Michael Faraday, the discoverer of electro-magnetic induction, electro-magnetic rotations, the magneto, etc.) it's true - this is the capacity of charge stored. They also have voltage ratings. The voltage times the capacitance equals the ENERGY STORED, in joules, or watt-seconds. One farad at one volt equals one joule, which is also one volt at one amp for one second... at this drain, this capacitor charge would last one second, and then be (for all intents and purposes) dead, until it is recharged. By doing the math, you can see that a 1 farad capacitor, charged to 14.4 volts, would be a total charge capacity of 14.4 joules. If you amp is demanding 300 amps from the power supply, it won't get it from the battery! - but the cap CAN deliver! 14.4J divided by 300A equals .048 seconds. This means the cap can supply 300 amps at 14.4 volts for 48 milliseconds - if you have two farads, that time frame goes to .096 seconds - almost one tenth of a second! PLENTY of time for the battery to come up with the huevos to supply 300 amps...
(side note: I have some capacitors at my house that are actually more storage capacity than that, even though they are only very small capacitance. They just happen to be rated at (one of them) 20,000 volts and 14 microfarads, but the other is rated 50,000 volts and 7 microfarads. I use them in parallel (21 microfarads at around 18,000 volts) to shrink quarters... pretty cool, really! These came from Lawrence Livermore Labs, and were used in the original Shiva Fusion Reactor Project, as energy discharge caps in the laser arms.)
A capacitor is built of plates - conductive plates and insulating plates - called dielectric, of which there are THOUSANDS - anything that is an insulator, from air to the skin on your hand - can be a dielectric, all with various characteristics that make them suitable for various flavors of capacitors. Capacitance is determined by how large the conductive plates are, (the surface area) and how close they are together - the larger they are, the more capacitance, and the closer they are, the more capacitance. If you want voltage capacity, you will trade off capacitance, because your dielectric must be thicker, to stand off the higher voltage, BUT if you make the plates bigger, you can end up with a capacitive value close to where you were before you desired a high voltage... The reverse also holds true - if you want higher capacitance, you can get the plates closer together, at the expense of voltage rating, but if you make the plates bigger, you will regain the lost capacity - are you following me?
The capacitors used for car stereos are low voltage, (EXTREMELY thin dielectric - so the plates are close together) but high capacitance - close together plus EXTREMELY large surface area on the plates; on the order of an acre or so - and I mean that literally - they get this huge surface area by acid etching the aluminum foil of the plates (and they use some VERY exotic manufacturing processes in the production of the foil as well) The motor start/run capacitors you refer to that your instructor showed you are (relatively) high voltage devices, which means they do not have much plate area, but the plates are separated by a fairly thick dielectric.
There is the long answer to your original question.
It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."