This article attempts to explain the different parts of a homebrew and custom firmware setup and where they are.
On the console: boot9strap
boot9strap is a firmware loader and exploit for the 3DS. It is installed into the firmware partitions of the system memory, also known as the NAND. This means that it stays even if the SD card is formatted, destroyed, lost, changed, or otherwise.
When the console is powered on, this is the first thing to be loaded after the BootROM. boot9strap then attempts to load a firmware file called boot.firm from somewhere else: first the SD card, then CTRNAND. If it can't find one, it will turn off the console.
On the SD card: Luma3DS
Luma3DS is a custom firmware. This is the most common firmware file to be loaded by boot9strap, and it is put on the SD card as the file boot.firm at the root.
During the final parts of the main guide, this is also copied to CTRNAND. This means the console would still turn on to the HOME Menu, even without an SD card (or with one that does not have boot.firm).