Is there a difference in how Ubuntu navigates in the Try Ubuntu mode as opposed to the actual download to your system mode? I would like to know before I actually download the full Ubuntu to my MacBook Pro operating system. The trial one I have in my system has a lot to be desired. Can both be kept as operating systems to switch back and forth?
When you boot a live session of Ubuntu using the "Try Ubuntu" option with bootable installation media, it is almost the same as an installed version of Ubuntu. The main difference is that a live session is loaded into RAM and is not actually installed to your hard drive.
The live session also doesn't retain any changes unless you have set up persistence. This means when you are using a live session, when you reboot, any changes you made during the last session will not be saved.
When you actually install Ubuntu, the performance is often better because accessing files on your hard drive is typically faster, especially if you have a SSD. With Ubuntu installed, you can also perform updates, install software, configure settings, and make changes that will persist after a reboot.
The live or try system is running from a squashfs which means your system needs to unsquash the files before they can be used, this can mean the system performs slower than a real install, however the difference will vary on what hardware you have (real disk, ssd, cpu etc) as Nmath said :)
Can both be kept as operating systems to switch back and forth?
You can use a live system anytime you wish, in fact I keep my thumb-drives as some tasks are far easier from live media than my installed system, eg.
changing partition sizes is easy from live media; but a problem if the partitions are mounted (ie. installed system)
performing tests for support; I usually use another test box with a QA-test install (Quality Assurance) but if I don't have one around; I can boot a live system on a box near me for that testing (a VM on my primary box would often work too)
testing out my own ideas is almost 100% safe on live media; as no changes are made (I don't use a persistent live image for this sort of testing) any changes lost on reboot or shutdown. This allows me to test out ideas first, before I try on my real installed system and risk needing to spend time fixing a mess I created.
fixing problems because of a change i've made; this is very rare; but as I know I can fix an non-booting system by booting a live system, I can experiment, test & play a little more as I have this fix option available
my system is already bloated enough (I have 3 full desktops installed), if I want to play with another DEsktop I don't have installed; I can boot a live session and use that for a day instead of my normal installed system.
I prefer using my installed system as it's fully configured to my tastes, where as live media boots up completely fresh. If you want to save configs on live media you can do that too via the use of persistence (I use mkusb). Yes you can use both.
Persistent Install vs Full install
Ubuntu can be installed to a USB in different ways. A Live install does not save between sessions. A Persistent install extracts the OS from a compressed file and saves data to an overlay file or partition each session, and a Full install installs the complete OS to the USB just like an install to internal disk.
The GRUB bootloader makes it possible to have multiple Live, Persistent and Full installs on the same disk at the same time.
Comparison between Persistent and Full install USB
Advantages of a persistent install:
You can use the persistent pendrive to install Ubuntu to another computer.
A persistent install takes up less space on the pendrive.
You can reset the pendrive by overwriting the old casper-rw file with a new one.
The install to pendrive takes less time.
Slightly less wear on the drive.
Advantages of a Full install:
You can update and upgrade.
If you have problems or wish to modify, the solution is the same as with an internal install, (You can ask for help in the forums).
No ugly startup / install screen.
Better security, you can use full encryption
You can use proprietary drivers.
Swapfiles and partitions work and Hibernation can be enabled.
Many persistent installs are limited to a 4GB casper-rw and a 4GB home-rw persistence file, to get more persistence requires persistence partitions. Once casper-rw is full, the drive will not boot.
More efficient usage of disk space. Does not require reserved space for persistence.
Faster boot, no automatic disk checking or Try Ubuntu/Install Ubuntu screen.
You can run VBox and use virtual machines.
Generally faster boot than Live or Persistent USB's.
More stable, better for day to day use. I have run Ubuntu off a flash drive for 5 years making only LTS upgrades.
Note that once booted, both methods run at about the same speed. If the computer has lots of RAM Ubuntu should run mainly in RAM and there will not be a big difference between running off internal HDD and USB3 flash drive f.
Full Install Method
A quick and easy method to flash a Full install to USB can be found here: Easy Full Install USB that Boots both BIOS and UEFI
A more traditional methods for creating a Full install USB from scratch can be found here: How to Create a Full Install of Ubuntu 20.04 to USB Device Step by Step