BIOS stands for Basic Input Output System. It is the computer system that does the very basic set up of computerized system. Some BIOS's can be altered by the user and some can not. Take an HP computer vs. a custom built machine with Asus motherboard for example.
In regards to a smart phone, there is a "BIOS" however you can not change it or update it, etc. It is hard coded into a chip on the phone.
The bootloader is the second step in the boot process. Many Linux machines use GRUB or LILO, etc. I imagine that SPL is the bootloader used by a smartphone.
I am not including i-phone type equipment in this explanation. I-phones run on magic and Skittles!! LOL