You are mistaken. Socialism is normally a broadly defined term which is why its understandable that people can make the mistake you say, but that didn't happen here, because we are talking about structure related to economics, and not political theory or ideology.

Importantly this is why Mises took such lengths in his works to define it consistently. It looks like you confuse the terms yourself, and not the other way around.

What it comes down to is whether or not there is private ownership, and ownership is the power of individual disposal. Without that power, you do not own anything.

Any limits on such rights and agencies, is the process of socialization, and when the names are divorced from such traditional terminology or handled over to another entity with new names, or same names but differing meanings, the old terminology or old meaning is essentially unimportant. What matters is the current terminology, and existing structure to the matter being discussed at hand, and when one uses the same words, they can easily delude themselves and others implicitly over those meanings, which is without rational basis.

The main nuance differentiating socialism from many other names/forms is in the ideology, or unrelated policy. These differentiations are unimportant to this discussion here, and muddy the waters for the people who have not educated themselves properly.

If the collective ownership in all things is in the hands of the state, this is socialism. Its important to be clear, socialism is not only an observable state (a noun), but also a process towards such a state (a verb). If it leads to, or is already in such a state it is socialism.

The money printer is state apparatus, the money printer decides and controls production by issuing debt, which eventually has a shortfall dovetailing into the many ways socialism fails. and by extension how society fails towards annihilation once production fails.

Non-reserve debt issuance is money printing. Reserve systems that do not account for subjective value are broken reserve systems that enable money printing. You can easily see that in 2020, the fractional reserve was set to 0%. It has remained there. They claim to have adopted Basel 3, but Basel 3 assumes objective valuations under Capital Reserve based in fiat, when subjective value was proved by Carl Menger, that industry will continue until there is a whipsaw or contagion and then it will fail overnight because of subjective value.

In true capitalistic exchange societies such property, including the means of production is in the hands of appropriate individuals, its decentralized, and these people are members of the general public as opposed to state apparatus.

When the majority of all property is in such money printing hands, where the debasement of all other goods occurs through currency, and worse fuels a sieve towards all property ending in such hands, this is socialism. The inevitable outcome is slavery for any but those at the top.

Eventually those people at the top cause collapse, they win so much that they lose, and that's because they don't have the calculation information to continue forward without shortfall.

Property obtained by these malevolent entities is property that has passed into the hands of the state.

When the market fails because its been sieved into fewer and fewer hands, to the point where independents can no longer profit. Producers leave, and all that's left is a collapse because its a faux market of state actors which is non-market socialism.

I would highly recommend you reread Mises's work on Socialism. Specifically Chapter 2: Socialism, Subpart 1 which covers these definitions and other common knowledge related to these type of discussions.

Malthus and the dynamics of depopulation describes why society would fail towards annihilation once production fails and people starve.