Both methods use a similar principle ...
Start with a base backup, which can take a long time to do.
This is a snapshot of your partitions at that time - just like a single standalone backup - which is what it is.
Over time your files change:
Differential Backup -> Backup changes in a new file since the base was made. Each time you do a differential it replaces the previous differential backup. This means you can restore your system back to as it was at the time of the last differential or the original base. Obviously the differential chunk will grow over time, and there will come a point when a fresh base is required.
Incremental Backup -> Backup changes since last backup. This is stored in an extra file, one each time you do a backup. These are usually quite small if you do them regularly and quite quick. Advantage is that you can restore your system to any of the times you did an incremental or base backup, not just the last one. Disadvantage is that it takes up more disk space than differential and you may need to do base backups more often to save running out of space.
It shouldn't take over an hour to do an incremental backup, and anyway you can continue to use your system while it does it. I do find the Acronis time estimates a bit hit and miss - my last backup initially said it would take 30 hours, after a while it settled down to 9 hours, and actually took about 3!
The really time consuming part is if you do a backup verify after each backup ... unfortunately Acronis have not realised that to verify an incremental backup you should only check the increment, not the whole thing. I have requested this a s a feature, but it hasn't appeared yet. PowerQuest V2i Protector (now sadly gone in to the giant dustbin called Symmantec) was great at this - a verified increment took about 5 minutes to build and verify, unfortunately it had a couple of bugs in its ability to create increments, and would occasionally decide it couldn't do it any more and start a whole new base backup - which defeated the object!
Note also that if you defrag your system regularly this will really bump up the size of your differential and incremental backups, as they are not stored on a file by file basis, but rather on disc sector by sector - so a defrag really has an effect on the backup size since it always compares to the base backup.
