Perhaps it all depends on how you understand these words, and what other people mean by them. Some people use the word ‘manure’ for chemical fertiliser. If you receive advice such as "it really needs to be mixed in", ask why.
With compost, it is not only a question of ingredients, but of process. Municipal compost needs by law to be free of pathogens (although many supposed ‘pathogens’ are, I think, beneficial to soil) so they make sure it has got really hot and this can destroy many good fungi and bacteria. Perhaps a little soil mixed in will then help it revive, or mix a little animal manure or garden compost, returning life to inert organic matter, which is perhaps what people mean by soil conditioner, something to give structure at least.
Good organic matter is full of life. For vegetable growing it is also well decomposed, dark in colour, not totally uniform, not perfect!