This is not accurate. Capitalism describes a system where people are free to own means of production. A hypothetical system where everyone owns some means of production, would still be capitalism.
No, it wouldn't, because it is marketable ownership of the means of production that defines capitalism; that is, it is the buying and selling, not the ownership alone, that is key (particularly, historically, the marketability of the means of production is a key factor distinguishing capitalism from feudalism, in which much of the means of production was owned but attached to entailments which the current owners were not free to alienate.)
For a version of your example, if everyone owned a fixed, equal share of the means of production which was not marketable, that would be an implementation of socialism.
I have to be sincere, I never saw this definition involving marketability anywhere, this is new for me. Perhaps it's really like you say, but that's not the definition I had, nor the one I see as the generally accepted one when checking up the definition of capitalism.
> For a version of your example, if everyone owned a fixed
But that is the thing, it isn't fixed. You are free to manage it, sell it, buy it, as you wish. That's why it's an hypothetical situation, where everyone would end up with a part voluntarily and not forced by the state.
> I never saw this definition involving marketability anywhere, this is new for me. Perhaps it's really like you say, but that's not the definition I had
But then also this about your hypothetical about a “capitalist” system where “everyone owns capital” which makes it capitalist as opposed to socialist:
> You are free to manage it, sell it, buy it, as you wish.
You seem to explicitly recognize that marketability—the right to buy and sell—is an essential element of the kind of capital ownership that defines capitalism in the same post that you claim that it isn't.
In any case, that is the reasoning of my second point when originally answering to you: A hypothetic situation where most people would own means of production, would still be capitalism when means of production are free to exchange hands.
That is too say: it's capitalism by definition as long as the means of production can exchange hands freely, it doesn't matter if they are all concentrated on the possession of a few or not.
If they can be freely exchanged, absent active as social management if distribution (which is not capitalism), they will become narrowly concentrated over time. Broad distribution is not a stable condition.
That's a fairly broad definition, so broad you lose all the meaning. By this definition, half of socialism (all but Marxism-Leninism) counts as Capitalism. Same for many economic system around the world since the beginning of History, while historians unanimously describes Capitalism as born in the late Middle-age/Renaissance in Europe (they don't agree where though, some talk about the Protestant counties (Max Weber), others think it was born in northern Italy (Fernand Braudel), while some consider the Jewish community as being the cradle of Capitalism).
I think your definition is highly influenced by the US anticommunist propaganda of the world war, who tried to create a dichotomy between Capitalism and the totalitarian communism. The reality is way more complex than this black-and-white narrative.