[int_19h]

By this metric, one can say that e.g. anarcho-syndicalists aren't anarchist at all, because their ideal society would end up as lots of small but totalitarian communities. Of course, the syndicalists themselves would dispute this, but then ancaps would also dispute your "corporate feudalism" claim.

The real difference here is philosophical. Right-wing anarchists believe that private property is a natural concept that exists independently of power hierarchies. Left-wing anarchists believe that's an artificial concept that requires such a hierarchy to enforce, and doesn't exist without it. Hence ancaps believe that absence of government will result in a capitalist utopia, while traditional anarchists believe that it would result in a socialist utopia. These two viewpoints are irreconcilable, because the fundamental premise is not just different, but literally opposite.

However, insofar as both groups believe that their ideal society is characterized primarily by the lack of a power hierarchy (and all other things, like unrestricted property rights, or complete lack thereof, simply follow naturally from that), both groups are "real" anarchists.