In Firefox, you normally only have one session; that session can have multiple windows. (In order to run more than one session simultaneously, you need to create multiple settings folders and use a special command-line switch to keep the sessions separate.)

Exit definitely means exit Firefox completely. However, using the red X should only affect that one window (the warning about closing multiple tabs should list the count of tabs in that window). I'm not sure why yours is giving you the same results as Exit. Maybe an add-on?

A standard diagnostic for add-on issues is to try Firefox's Safe Mode.

First, I recommend backing up your Firefox settings in case something goes wrong. See Back up and restore information in Firefox profiles. (You can copy your entire Firefox profile folder somewhere outside of the Mozilla folder.)

Next, restart Firefox in Firefox's Safe Mode (Diagnose Firefox issues using Troubleshoot Mode) using

Help > Restart with Add-ons Disabled

In the Safe Mode dialog, do not check any boxes, just click "Continue in Safe Mode."

Any change in red X behavior?

>> (In order to run more than one session simultaneously,

    >> you need to create multiple settings folders and use a 
    >> special command-line switch to keep the sessions separate.) 

All is well, thank you for your assistance. I am not sure what or how the 'problem' was created. Can you please direct me to the command-line switches (direction) you reference above? Thanks again, J

Please see cor-el's solution in this thread: https://support.mozilla.org/en-US/questions/925594#answer-327043