TL;DR: Is it possible to define hierarchy, as a useful term for communication and association between anarchists? If so, what are some of those definitions?
There are many different strains of anarchism, and specially since anarchists mostly believe in decentralization, I feel like many of our efforts go diluted for lack of collective organization. Sure, there are big anarchist collectives doing work out there, but I have the sensation that most youth or influential people who identify themselves with anarchist causes get lost in the plot simply for lack of a bigger movement. For most of the modes of anarchism there is one big bad evil guy, commonly named "hierarchy"; although writers and academics define those terms in their publications, I can't help but notice, at least in the forums I've been around, your average anarchists could be talking about two completely different concepts of hierarchy or oppression. Maybe if we had agreed upon definitions to those hot topics it would be easier to associate. Is that even possible? That we all agree on the same meaning for a word? Do we call Chomsky to solve this linguistical issue?
Or am I completely wrong in my questionings?
I think it would be a very good idea to make the link between the notion of 'hierarchy' as anarchists like to think of it and coercion a part of common knowledge, both inside and outside of the anarchist community. I think everybody being on the same page with terminology would help clear up a lot of miscommunication about anarchism.
I don't think that this is the primary problem that we're facing, though. I think that part of the reason that it is difficult to pin down a definition of 'hierarchy' that everybody agrees upon is because there are some 'anarchists' that don't actually want anarchism, but instead want a lack of personal accountability - in other words, the freedom to do whatever they want to whomever they want without consequences. If you frame this in terms of 'personal freedom for everybody', it sort of sounds like anarchism, but because it emphasizes positive freedoms to the point of discarding negative freedoms almost entirely, it actually ends up being a self-contradictory position where bullies have power because they're willing to penalize their victims into submission, and there are no collectively-enforced consequences for engaging in such oppressive behavior.
I think that the #1 problem that we need to solve is the issue of these individuals generally being an accepted part of our group (or society at large, even). Anarchism isn't actually a magic bullet for oppression, because even an anarchist society would eventually be corrupted into an oppressive one if bullies like this are allowed to persist and manipulate people into following them and their disordered ideology. To actually create a truly 'good' society, we need to learn how to reliably recognize these bullies and keep them out of our spaces. Anarchism helps enormously, because collective power is much harder to subvert than hierarchical power, but it isn't a complete solution on its own.
That said, being able to recognize coercion and manipulation in all of its various forms would help a lot with that goal, and so the goals of establishing such a common terminology and also teaching people how to recognize bullies in all of their various forms are synergistic.