Rsync has a number of flags which control what it will look at and what it will copy over to the destination. Most often the "-a" flag is used which is the "Archive" flag, this is probably what you want. run rsync with the "-av" flags and have it do a first run against the data you want backed up. The next time it runs it'll do a block checksum of the file, and only copy over the parts which have been modified on existing files, copy new files over, and remove files which are no longer there. Check the "-a" options section on:
The first run will be BandWidth intensive, the following runs will most likely be processor intensive but use little Bandwidth compared to the initial run. Unless you have a lot of churn over your data set.
Rsync doen't care how you got the files in the source, or the destination directories, it's only going to copy the changes between the two, unless you add flags to do something different.
If you want to log what was changed you can use the "--log-file" option. All in all something like this sounds like what you want:
rsync -av --log-file=/var/log/rsync.log -e "ssh -l backup-user" backup-user@source-machine::module /nas01/backups