Can socialism and capitalism basically be boiled down to the ideas of "Let's share" vs "Don't touch my stuff"?

So socialism has capitalism at the bottom and the sharing layered on top of that?

No.. Socialism is how services and support are provided, usually derived from Taxation.. Capitalism is one way to generate the income and therefore the tax revenue.@plungesponge

So, capitalism is the taxation input and socialism is the sharing output? I understand the 2nd part but not the first part. Is there an example that shows how this works?

Swedes Danes and Norwegians pay much higher income taxes than many OECD nations... But Housing Power schools and the health system, plus aged care are all heavily subsidised and not much cost to the user.. Through the social support networks.@plungesponge

Thanks for that. So it sounds like taxes are higher to provide more services. That seems clear though I'll admit I don't see how that is different from the concept that socialism is about group sharing and capitalism is about personal ownership

It depends on how far you take the concept.. It can be like a Kibbutz if extreme.. But mostly its about government providing the major "Public good" services. Like Health education infrastructure and public housing.@plungesponge