How is Firefox Portable and Thunderbird Portable different from Firefox and Thunderbird on the desktop

No difference at all in the actual application. The portable versions just include a launcher written in NSIS scripting language to back up any settings that may exist on the host PC, apply your portable settings while the app is in use, then restore the host PC's settings for that app. Also, any registry entries or info in the Application Data folder that was created by the app is cleaned up after use.
_____________________________
I don't believe in signatures

Differences: The portable versions of apps can run on a removable drive, ie usb key or external hard drive. They also do not leave anything on the host computer.
Similarities: Most of the apps are the "desktop versions" with a special launcher that saves the settings and clean up anything that the app left behind.

Once you have the portable version, you do not need the desktop version, but I would recommend keeping the desktop version on your own computer simply because it will launch and maybe even run faster than the portable version.
═════════════════════════════════════════════
There are 10 kind of people in this world: those who understand binary, and those with friends.

I see things just the other way around and do not keep a desktop version of FF and TB on my PC anymore.

I use the portable versions on my PC as well as on my USB-stick. It is true, that running a portable app from a stick is a tad slower than running it from off of a harddisk. But I seriously doubt that anyone would sense a difference between desktop and portable versions of a programm if both are running on a hdd. One thing you should not do though is to run both versions side by side.

Using portable versions on your PC is the most convenient way to keep its registry clean(er) since portable versions do not need any installation. You simply unpack them into whichever folder you like and that's it. To get rid of a program you simply delete the folder you have unpacked it to and you are done...

...with portable apps, since they don't modify the registry, so "double clicking" will continue to use the defaulted program to open a file.

But, Not a problem, since "File...Open..." and drag-drop work perfectly once you open the portable application you want (easy with Portable Application Menu). Just be cautious to "drop" your file on your application and not into the host's file system somewhere (which would be putting a copy of your file there!)

(Also, there may be utility programs to make temporary file associations. You might find something discussed -- use the "Search" at upper right. I don't think there's anything yet on the Applications menu)