As far as I'm concerned, compost and fertilisers are two different things.
Compost is, at its basic definition, no more than a growing medium.
It may contain nutrients and trace elements, but that is a fortuitous extra.
"Fertiliser" has become a pejorative term, due to the petro-chemical type, which may help short-term, but aren't nice in the long run, but to me "fertiliser" means anything which makes the growing medium more fertile, and that includes all the organic and wholesome additives to our growing medium.
I use seaweed, wood ash, horse manure, and compost tea, all of which I make myself, and all of which I regard as fertilisers, but as I cannot make enough for my needs, I tend to supplement them with ORGANIC fish, blood and bone, and chicken manure, and volcanic rockdust for remineralisation.
That is not to deny the value of compost.
On its own in pots, or in conjuction with the soil, it provides an excellent home for my plants, and prevents the soil, and its beneficial microbial community, from becoming depleted with continual use, and, in fact, enriches it.