No, all human groups of almost any size have hierarchies of one sort or another though they can be fluid or dynamic. That appears to be a property of higher primates anyway.
Ignoring the De Jure (or De Bello) aristocratic and 2e Estate ranks, jobs were pretty loosely connected at best to one's "rank" in medieval society, in particular in the countryside. Certain jobs had a cap ex element (miller in particular, but smith too) but that would likely have been the property (and investment) of the local squire or lord, not the property of the operator.
Even the jobs you named such as cooper, baker etc tended to be tied to urban societies (towns really), and a farrier was sufficiently specialized to be in the court, but not to have any sort of special grade or rank.
In the later Middle Ages as the growth of the guilds and cities began to challenge the aristocracy, rank still depended more on wealth than job (an inversion of the aristocratic order, and that of the Roman republic and empire, where you became wealthy though power rather than the other way around as today). But even there we're talking about a small number of people; being a baker or miller wasn't really a self identity in the way we think of it today.
And there were people assigned job-related surnames as a tool of scorn (Goldschmidt -- goldsmith) where there were jobs reserved for specific outcasts (i.e. jewish people in Europe): again they had those jobs as part of bing an outcaste group; they didn't become outcastes by having those jobs.