AFAIK, Deja Dup backs up files and that are in the home folder to say a USB drive (except for those that are ignored) whereas Timeshift creates snapshots of the WHOLE system and records them onto your system so you can restore it using a live USB.
I'm probably going to get yelled at for this, but I've never used Timeshift. Ever.
I have used both and my complaint with both is pretty straightforward:
They take up a lot of space. Timeshift takes up more since as you say; it creates a whole snapshot.
And both can cause data loss since they compress and encrypt the data.
This is a viable trade off as a solution for many people. It isn't for me, though. I backup and save only the working files I need.
It is a little extra work to reinstall my software - but I have a thread with two quick commands to make that easier.
And I do not have to deal with either bloat taking up a lot of extra space or the risk of data loss- since I link backing up my work only in two different places. One is my own sync cloud.
Really? I didn't know that.
Well, I encrypt my backups (that's a viable option in Deja Dup) and I haven't had any data loss... yet.
I'm not saying this is not going to happen BTW.
I do the same thing as well. Though, I've moved cloud storage recently.
I backup my user directory daily with Deja Dup. I used to use Timeshift when making major changes to my system but I am no longer using it because I am happy with my current environment. I don't know why, but Timeshift does not recommend taking snapshots of user directories.
That's kinda ludicrous if you ask me.
Another point: Deja Dup backs up to a secondary storage (such as Cloud and USB) whereas Timeshift backs up to primary storage.
Ditto. I completely submit about 95% to the tyranny of defaults, and now that I no longer distro hop, the only thing I'm concerned with are my files. They live in a remote Nextcloud directory, and I use Deja Dup to backup to an external HD now and then, and that's only because I'm a belt and suspenders kind of person. I've never used Timeshift ever, either.
This cracked me up.
It then brought to mind the scene from "Once upon a time in the west" when Henry Fondas character (Frank) says... "how can you trust a man that wears both a belt and suspenders? Man can't even trust his own pants."
I love this kind of humor.
I think the correct term should be "belt and braces".
Personally, never liked Deja Dup - it was never clear what it actually did - think I tried it once on a much earlier version of Zorin - I stay clear, just like I do Fedora!
It has to be a combination of: Rescuezilla, Timeshift, backup of /home to external device before fresh install/upgrade.
Belt for trousers, Braces for trousers, suspenders for men's socks - not pants!
Where you live, folks call the trunk the boot, the hood the bonnet and a packet is a sachet.
The driveshaft is called the propeller.
The windshield is called the windscreen, the Alternator is called the Dynamo... You call a wrench a spanner.
You call fenders... uhh... wings...
Let's not argue over culture terms.
I always thought fenders were bumpers in our parlance! 
Hence the term, fender-bender - or ... an accident waiting to happen!
To me a packet is a packet (packet of crisps = chips). A sachet is like "a sachet of shampoo" or something that contains a lense wipe - that is a sachet.
For me it has always been the driveshaft - from engine to the driving wheels, my prefernce was for rear wheel drive as you could deliberately on a quiet road junction practice skid control in the snow and start off in third gear before clutches became rubbish electronic ones with no 'bite'. An alternator is an alternator here - the only thing I know of as a dynamo as a kid was a contraption that had a wheel in contact with a bicycle wheel that powered the bicycle lights on my dad's bicycle. On a motorbike, the alternator is termed a rectifier.
Yes, I'm afraid that was not one of the words that divides USA v UK by a common language.
Once upon a time cars had Dynamo's (d.c. current generators) then along came Alternators (a.c. current generators + rectifiers). So we have used both words here in UK, but for different things.
Aravisian could have used Elevator v Lift as an example of USA v UK English
Australian English is also littered with alternative words, but let's not get further sidetracked from OP.
Ooops.
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