Well if you are using standby and you arent draining the battery, you are very lucky :-) Maybe you use the car every day, for extended periods? Because if you park most vehicles for a day or two on standby with one battery in the car, it should drain it.
I think most people probably use hibernate. It takes a very small amount of time longer to resume, but you use less (almost nill) power.
Some PSU's monitor the voltage and send the shutdown command if it drops below a certain level. Is it possible that you are shutting the car, its going into standby and later when the voltage drops the PSU is putting it into hibernate. Could it be that you are not noticing it resume from hibernation sometimes?
No other ideas.
Sorry you asked about the main difference.
Standby : The CPU goes into a low power mode, the display is shut down, the ram stays powered. Very quick return to operating state. Uses less power than when its running but still actively using power for ram and other things.
Hibernate : a picture of the system state (what programs are running and the information in ram) is saved to the hard drive, then the system is shut down (all the way down, you could pull it out of the car and put it back in and it would resume right where you left it). When you start back up, the MB goes through POST, then the image of what belongs in memory is loaded from the hard drive back into memory. This happens a whole lot quicker than rebooting windows and initializing all the drivers and such. Theoreticaly uses zero power while hibernating.
( I only say theoreticaly because some PSU/MB cause a draw, albeit a very small one, just being connected to the system). I cant explain this, its like putting a small light bulb on the end of a thousand foot wire, if you shut the light, for some reason the battery will drain faster than if it wasnt connected to that wire. (not an engeneer, just stating what I have read).