I'm not sure that the pathway to domestication is always the same.
The problem is that with the exception of rattite birds in the 19th century, every major domestication event took place thousands of years ago, in remote regions, with no tradition of literacy and very poor archeological data.
So we tend to assume, or hope that there's a 'master theory' of domestication, where the pathway for horses, cattle, sheep, reindeer, goat, water buffalo. llama, swine, camels and yak are all similar. There may be something to this - many of these animals show overlapping characteristics - they're large, herbivores, used for draft or labour, sometimes with secondary features, typically milk or wool.
The majority are grazers, though some are browsers, a number seem to be migrators or potential migrators, though some are territorial. Some seem affiliated with agricultural societies, but some were clearly domesticated by nomadic hunter/gathers. I think that there may have been distinct pathways for agricultural and nomadic societies. But it's hard to say.
I'm inclined to think that the relationships are commensalist - ie, animals are habituated or tolerant to humans and find advantages in hanging around with human society. But how commensalism evolves may be variable.
As to other domestications - cats, chickens, dogs, microlivestock, etc., almost certainly variant pathways.