A decade ago in secondary school I learned of capitalism as an economic system where [the vast majority of] the means of production are privately owned and oper

A decade ago in secondary school I learned of capitalism as an economic system where [the vast majority of] the means of production are privately owned and operated for profit through the purchase of labour, and of socialism as a broad umbrella term for economic systems where the means of production are socially owned (and that there are various kinds of social ownership) and self-managed by labour itself. As far as I am aware these are the definitions that have been in play for the century and a half or so that the theories have even existed. In my experience they only get weird redefinitions (such as socialism apparently being "whenever the government does something") in particularly polarised countries (cough the US cough). Sure, people arguing from ignorance or disingenuity are technically having a debate, but why on earth is everyone listening to them? Beyond that, speaking more precisely about tax policies (statism), free market competition (market economics, laissez-faire) and safety nets (social welfare) is an endeavour all societies should partake in, sure. But it's also orthogonal to the axis of capitalism vs socialism. Having a higher marginal tax rate, regulating markets, and/or implementing a welfare state doesn't magically remove the private ownership from a capitalist system. Similarly, charging no taxes (or even not having a state at all), operating a free market and/or not having a social security system wouldn't make a system that runs on social ownership any less socialist. It's like attempting to resolve a debate between functional programming and OOP by saying we should focus on specific elements of the two so that we can speak more precisely about things like static/dynamic typing instead. That does not answer the original question at all.