The two versions are installed in a different location.

• (32 bit Windows) "C:\Program Files\Mozilla Firefox\"
• (64 bit Windows) "C:\Program Files (x86)\Mozilla Firefox\"

You can consider to edit the name in the desktop shortcut and add 32/64 to distinguish them.

You posted this question with the 32 bit version: User Agent: Mozilla/5.0 (Windows NT 10.0; WOW64; rv:43.0) Gecko/20100101 Firefox/43.0

32-bit versions of Firefox have "WOW64" in the user-agent.
64-bit versions of Firefox have "Win64" in the user-agent.

You can find the user agent on the about:support (Help > Troubleshooting Information) page.

When downloading installing programs, I sometimes find that the filename is not descriptive enough. So after the download, I will change the name by adding the program name and version in front of the filename that was used.

When installing most programs, you may have the opportunity to change the folder the program is installed to.

Hi,

Firefox Team please change the Name for 

Firefox Setup.exe {For 32 bit version} Firefox Setup64.exe {For 64 bit version}

It will help to manage and install easily for IT Professional's.

All the basic software's have the different name for 32 bit & 64 bit. But Firefox having the same name for 32 bit & 64 bit.

Firefox Setup 44.0.2.exe {32 bit} Firefox Setup 44.0.2.exe {64 bit} googlechromestandaloneenterprise.msi googlechromestandaloneenterprise64.msi AdobeAIRInstaller.exe install_flash_player.exe install_flash_player_ax.exe install_flash_player_ppapi.exe jre-8u74-windows-i586.exe jre-8u74-windows-x64.exe Shockwave_Installer_Full.exe Silverlight.exe Silverlight_x64.exe SkypeSetupFull.exe vc_redist.x64.exe vc_redist.x86.exe vlc-2.2.2-win32.exe vlc-2.2.2-win64.exe winrar-x64-531.exe wrar531.exe

Thank you...

edit removed link J99

The files are downloaded via different links or from a different directory on the server, so it shouldn't be too difficult to save them to a different folder and rename them yourself.