At someone's suggestion on this forum I decided to try LinuxMint on my machine that I use for trying other distros. LM has updates almost every day just like Z16. But they WORK! I have not had any problems with the update function on LM. I wish the update function on Z16 could be made to work as well as the one on LM.
There have been other threads about the updater included in Gnome-Software and its quirks. And it is noteworthy that the gnome-software updater is not the same as the System Updater included in Zorin OS.
The best way to save yourself a headache on this is to run the command @Adithyansm posted above in terminal. Whenever you feel like it, really...
I do it often because my participation on the forum makes me have to do it all the time, testing things and such for other uses. In this advantage, I am spared of having to make a routine of it.
But you can make a routine of it, or just open Software & Updates and set that to automatic updates, too.
I did run the terminal commands and that did solve the problem. I have auto update turned on but it says that is for security updates not in general updates. I get from time to time a notification that I need to install updates. When I click on that notification I get the screen I posted a screen shot of in my first post. I then click on update all and get the message you see in the small black window. Also if I just click on the software store to see what I might want to install it shows I have updates there also. But when I try to update them I get the same message. Running the terminal commands has fixed it for now but I am pretty sure I have done that in the past and after a while the problem comes back again. I will bookmark this post so I can come back to it for the terminal commands if the problem returns.
I hear you Carroll. I get them too. Sadly, it's not a Zorin issue, but they will
be blamed...lol I try not to use snap or flatpack whenever possible. But sometimes, ya just got to.
When snap checks versions of software it doesn't check what kind of package installed it, so you may see updates available for packages that are not flatpak/snap. This is because the versioning for each package type is different. So a .deb package will be at version 4.2 and the snap is at 8.3, the snap store will insist you have updates though it has nothing to do with that software because it's not snap.
It's an annoyance we must endure until the developers include a check for what kind of package it is. Sometimes running the terminal commands won't fix it because there are no updates for that software in that package.
I avoid snap and flatpak (neither are on my system) and it negates my need for the software store. I search the web and install by deb or apt. Then all my software is updated by the terminal command.