How do I find the differences between macOS and linux wifi drivers on mac hardware?
According to Debian, Broadcom has added support in WL version 6.30.223.248 for both hardware versions of your card - PCI IDs 14e4:43a0 and 14e4:4360
If you still need to find out exactly what version do you have, boot into Linux and run
lspci -nn | grep 0280
If you are going for a fresh Debian install, make sure to add the non-free category to /etc/apt/source.list to get the proprietary Broadcom driver.
What is the difference between the Card Type and the Firmware Version?
The Card Type field shown in "About this mac" appears to be broken. It seems to be combining the card's vendor ID with the subsystem vendor ID, which may or may not uniquely identify the card, and even if it does, only to the system vendor's native operating system.
The firmware version is the version of the firmware running on the device. A wireless card is sufficiently complicated that it has it's own CPU inside (for example, a microcontroller). The firmware version identifies the software running on the card's CPU.
Is the Firmware Version another word for a Driver?
No. The operating system driver runs on the main CPU. It is responsible for interfacing the OS to the PCI bus. The firmware runs on the wireless card. It is responsible for interfacing the PCI bus to the actual wireless radio hardware. It is kind of like a "driver" in the end, except you don't want to call it that because it would cause more confusion.
You can think of the PCI bus as a telephone line between a house (OS) and a nearby shed (wireless card). The driver is in the house talking on the telephone with the firmware, which is in the shed. The driver is subordinate to a chain of command in the house, but the firmware is king of the castle in the shed.
The situation is further complicated by the fact that many cards do not include the firmware on the card itself; the card itself just has a kind of bootloader that can load the firmware over PCI and then execute it. So you have to have a compatible firmware file on the OS side and the OS driver needs to know how to feed it in to fully bring up the card. But the firmware does not run in the OS, it's just fed to the card without (too much) processing.
Which terms in the output of lspci -k correspond to the output from "About this mac"?
None of them. Intel Corporation WiFi Link 5100 should have PCI ID [8086:4232], and definitely not a match to PCI vendor 0x14E4 (Broadcom). You're hitting different hardware from MacOS as from Linux; the complete output of lspci -nn might reveal what is going on.
How do I know what driver to install?
The card you did find in Linux has already been claimed by iwlwifi. If you can get running with that it's probably better to do that as the Intel cards have better Linux compatibility than the Broadcom ones.