sleep vs hibernate

I do most of my work on a mac mini and have an external drive hanging off it for backups. I also have a macbook pro. I would like to have the macbook backup to a partition on the external drive. It seems that when my mini goes to sleep after a specified time the macbook backup continues. This sort of tells me that the mini can still do some processing. If I don't wait for the sleep to kick in and I perform a command-option eject the mini immediately goes to sleep and the macbook backup halts. So am I correct to assume that these 2 types of "sleep" are different? Maybe one is a sleep and the other a hybernate? If this is the case when the system "falls asleep" after a specified time, does it ever go into a hibernate mode or will it always be able to perform network tasks?

much thanks for the help
john

so, here's the deal, I set the computer sleep and display sleep timeouts to 1 minute. After a minute the monitor went blank as expected. I waited another 10 minutes just for giggles. I was still able to access the mini's external drive. One thing I did notice is that when I put the mini to sleep with the command-option eject sequence the light on the front of the mini starts to very slowly blink. When the mini goes "sleep" after the timeout the light stays on. I know there are ways to run linux based commands to change the sleep/hibernate levels so this might be a case of different levels of sleep. I will have to perform a test tonight to see if the time out sleep mode ever switches to the blinking kind of sleep.
thanks for the help
john