Trying to understand the 2 directions of a backup-from A to B & B to A

I create a back up and then in due time the original files are either renamed or moved or deleted. Would I be correct in assuming that the backup copy could not know of these changes. In other words when it's time to do a 2nd back up, I believe at this point it would be called 'Incremental back up if one does not want to copy over the same files, then changed files would be copied over the original files would they not? thus giving you 2 copies of the file (the 1st one which you named abcd.doc and the 2nd one which you renamed, fgh.doc) And also if you deleted some files in your original then when you make a 2nd backup, the backup would not delete as well this file.
And vice versa as well (from your backup to your PC).
If this sounds confusing, I am assuming that outside of full backups, it is not possible for backup software to determine what files have changed name or place and can not tell either what you deleted and still want or don't want. [A reply to this will help me determine a new strategy of naming files renaming etc.] Thank you

Thanks and sorry for the confusion. By back up I mean (data) backing up my folders which contains movies, photos, Word Doc files and stuff like that. As to why I rename--well for example I may upload files from my camera which by their defaults are just a few letters and numbers. If I do my back up then, these files, are meaningless until I see them. Hence, they would be changed to something meaningful like MimiAtThebeach.jpg (Yes, I do usually rename them before a backup but don't always have the time to do everything at once) OR what also happens is that after a while I realize the naming is not good enough and rename it to something like Holiday-Haiti-2013MimiBeach.jpg But how, why and when I rename my files is not the question here is it? As to SyncToy thanks- I will look into it. Now I've been using 'Coybian BackUp' which I find too slow--and am presentl trying BackUp Maker and see how that works.

Backing up is making an extra copy of whatever you think it's ie a file, a pic, a folder, a whole disc, a whole whatever.Blah!blah!blah!blah!.

If you back up another copy of a same item without changing the name, the new item will overwrite the old item.
For example: Mimi.jpg saved on 6th Dec. raw will be overwritten by Mimi.jpg saved on 7th Dec after being edited when you backed up.
However, the story is different is you save it on a different folder, partition, or HDD, and not the same HDD or partition.

Imaging in a different partition or HDD will be easier as the file will not be overwritten unless you forgot and write on the same partition.I did that once and boy that really wasted my time. For example, the first imaging was Jan-June 2013 and the second imaging is from July-Nov. 2013 all the same items but on different partition.

Thanks people Truly appreciate. Am not sure what an image is. I thought it was taking the whole thing, like your C: drive and all its settings, registry etc. And did not think an image could be just for data files so now am need to look this up I guess. I do, BTW have all data in different hard drives, partitions-- Audio-video stuff in one. and ebooks, word docs and software in another. My backups go on one internal hard drive and 2 external hard drives (no longer take chances after having lost 700 Gig worth of stuff years ago. And it is about 700Gig in total that I back up (I have a huge photo collection (200 Gig or so) and MP3 collection as well as movie collection (Transferred from CDs, VCDs, and DVDs) and all my software is legit-legally bought as well, which includes Adobe Suite and Office Suite