We have a different Canon (MG5350S), but with a similar set of inks.
The PGBK one is the large black - which is used for printing things like text. The small black (BK) is used for adjusting the colour shade. The light being on indicates that cartridge is out of ink (or thinks it is). And these printers generally refuse to print at all if one cartridge is empty, even if that cartridge isn't needed for the pages you are printing.
My Canon Pixma is happy to print while fibbing to me that my PGBK is empty. The PG indicates pigment ink, by the way, the other black and all the colours being dye inks.
In general, printers don't actually know whether cartridges are empty or not as they have no direct way of measuring the contents. Instead, the printer maintains a count of how many droplets of each colour have been used, and that's used as the basis for the "low" and "empty" warnings. Test pages are a more reliable way of checking ink status.