You probably know everything I was writing in my response and more.
because there has been a lot of activity in the area of new file systems to solve new and interesting problems especially involving combining (or other things) - filesystems I would look on kernel org first.
Index to filesystems new and old with descriptions:
https://www.kernel.org/doc/Documentation/filesystems/00-INDEXI don't think you were getting at virtualization or containers.. (although they are where I would go to do the kind of incremental snapshot thing you're describing, thats one of the things a fairly feature rich virtualization tool like virtualbox does best, Docker is a popular container format, not the same thing as virtualization at all but it allows you to create a self contained virtual appliance that can be very convenient and portable)
Do you tend to use one particular distro? If so maybe your distro has a particularly appropriate tool. Ive never used the one that I see in my package manager on my distro the most Debian - bilibopfs) so I have no idea if its what you want.
You're discussing two totally separate things- right? Portable apps (Appimage is one format) let you carry the app and all its config files around and run it on whatever machine you're using.
I don't know where Knoppix is these days but back in the day it was a great tool to have handy as well as a good example of how much functionality and drivers could be crammed into the space available on a single DVD or CD. Also it could save its changes to a separate USB flash drive. Now probably almost all LiveDVDs and CDs can do something like that. the ways they handle file systems vary though. What you seem to be getting at is you want your current work to be portable so even if the client wont let you boot your own liveDVD or if you use their OS, you can still use your files interchangeably?
I don't know enough about what you want or this subject to be as helpful as I would want to be. Other people here could probably do much better. Sorry.
DistroWatch if you have the time and bandwidth, could let you try out a bunch of different LiveDVDs, fast.
How can I save/restore the whole OS while working with a Linux started from a Live CD?
USB install - not good
Live USB with persistence - not good
Custom made Live CD (with personal settings and extra programs included) - not good
I want to save a live session at request, as in live Puppy Linux that can save all at shutdown of a live session.
The main idea will be to have:
1. The unmodified ISO or CD/DVD media with a known Linux distro and
2. Another USB stick with all the extra settings and extra tools for that particular Linux distro
3. The setup is not supposed to be a full PC, just a temporary tool to configure some onsite equipaments
I want to use this combination of 1. a standard install DVD + 2. my USB with my previously saved live session at the client side, OFFLINE (no Internet), for example in places where one is not allowed to bring own laptop, but it is allowed to use a local PC, and boot it from the client's trusted installation DVD media (unmodified Ubuntu 18.10 install DVD).
If you have a fast net connection I would go to distrowatch.com and download a bunch of liveDVD and liveCDs, whatever seems like it might be good, and just see how various task-specific distros manage to do it (all sorts of different ways) and see if any of them seem like thats what you want to do. If it is, likely you can just do that, either with that distro or adapt it to your own.