In terms of Linux TPS
firmware is an image you may upload into TPS with bootloader
(using bootloader CLI or firmware automated update feature)
or XModem/Ymodem protocols.
Firmware image can include bootloader update, kernel binary or the whole operating system image all-in-one file,
while the Software is an individual package(s) that may be installed into the running operating system.
Please, keep in mind that firmware updates may be performed only from the bootloader in semi-automatic way (by pressing MD button while TPS is starting and preconfigured update source is available) or manually from serial console and will completely rewrite some parts of NAND flash. So please, read carefully the description of the firmware update file: what this firmware update file contains and would you need to reconfigure your Linux TPS after this update?