You will lose your bet.
Linux uses packages for instillation and depending upon how the individual packeger puts the install package together will determine if the program will install in the menu.
I just installed FireFox on a new Raspberian system and it appeared under the Internet category as FireFox ESR.
At one time there was Iceweasel version of FireFox, but that is now considered transitional and can be removed.
You can use the supplied pi-packages GUI to search for and install programs. This program is under Preferences on the menu. Some like to install Synaptic as the GUI for adding, updating and removing packages. Both programs list dependent packages, so it can be hard to find the correct program to install. I find using the list at Raspberry Connect
is helpfu to locate a specific program but it may take some digging.
With post IBM 360 MVS OS code is written using function modules so the code can be reused and by passing different parameters one can adjust what files, fields, variables etc are processed and these functions can report the success or failure of the funciton´s processing. When the basic task are called through a GUI the programmer can chose to suppress the return messages. It turns out the apt-get install, pi-packages, and synaptic all use the same basic functions. ¨apt-get install" list each individual task and result, ¨pi-packages¨ only creates a log, and ¨synaptic¨ has an option to display the task messages during the install. So all 3 programs perform the exact same task but each a little differently. Sort of like providing turn by turn instructions vs. providing GPS coordinates for driving instructions. Both will get one to the destination but the recipient of the instructions will need to understand how to use the information.
Many volunteers have worked hard to take Unix/Linux from its command line start to get it to where it is more user friendly now. At least for some tasks.
f u cn rd ths, u cn gt a gd jb n cmptr prgrmmng.