Physics of batteries (volts vs charge) Car batteries are usually 12 V. What is the difference between buying a car battery and hooking up a bunch of cheap household batteries in series? Both would register at 12 V. I assume that cars need much more current to start an engine then regular household things like lamps and toys. Does that mean that a car battery holds more charge within it?
If we think of a simple cell battery, where there are two electrodes and an electrolyte. One electrode eventually, through chemical reaction, becomes positive and the other becomes negative. Thus in a car battery, does that mean the electrodes (if we can reduce a car battery to a primitive cell), have more charge separated on each electrode? But if that was the case, wouldn't a greater charge separation mean that the voltage would be greater between the terminals as well?
In general, what is the relation between charge and voltage? I know the equation V = U/q, just like E = F/q (similar form, in the limit that the test charge is small as to not effect the PE or electric field. V = U/q is sorta useless too, since differences matter, but nevertheless that is how we defined it). If charges are separated further, does that mean greater voltage? If more charge is separated, does that mean greater voltage?
Lastly, what is the difference b/w the charge in a 12 V car battery, and the charge in a 12 V makeshift, series strung battery from home? 
 A: You asked too many questions to make sense answering individually.
12 V is 12 V, but what distinguishes a car battery from a bunch of AA cells strung together is that it can still maintain this 12 V at high current, like what a starter motor requires to crank a cold engine.  Actually even a car battery will exhibit a voltage dip when the large starting current is drawn.  Dropping 2 V during starting is not out of line at all.
If you were to string a few AA cells together to make 12 V and hook them up to your car instead of its normal battery, the voltage would go down to essentially zero when the starter was turned on.
Car batteries also have much higher capacity than ordinary houshold batteries.  A rechargable AA cell might be good for 2 A-h, whereas a car batter could be around 50 A-h.  This is the total charge the batter can deliver.  This is a separate parameter from maximum current.  Car batteries are usually sold with two specs, cold cranking amps and Amp-hours.
As for the charge on the electrodes, you seem to have some confusion.  In most batteries, typical lead-acid car batteries included, the energy is actually stored on the surface of one of the electrodes.  In a car battery, this is when a chemical change occurs on the surface of a lead plate.  The maximum charge storage is therefore proportional to plate area, which is why car batteries are the size they are.
A: Hello this may not be the answer you are seeking but i cannot comment and i would like to try helping you with the question so...
I just researched more into the subject and found out about what is called Voltage Drop which means when the amperes go up high the voltage starts to drop and some cars need as high as 300 and 400 in cold weather i am now working on numbers for that will update when i figure the miss up!
