I think the defining difference is whether that sharing extends to just friends and family, or if it becomes more egalitarian and extends to everyone. From my experience, Republicans tend to stop at the former, and Democrats tend to stop at the latter. There is also usually differences in what they’re willing to share to both parties, namely money.
I live in Florida, surrounded by red and I’m from a red state/area. To be clear, I think it’s PERFECTLY VALID to hold the thought “my money and stuff are mine and I should have a say who gets to use it”. And to your point about democrats: yeah that’s effectively what I mean. Universal health care and paying for college are publicly funded from…other people’s money. Most Republicans I’ve talked to wish we had either or both, but balk when taxes are raised. They would rather be the ones to decide who gets a portion of their paycheck from an understandable hesitancy to have the government be the one to decide who gets the money. Republicans see that prudence as necessary, and most democrats I know see that as an unwillingness to contribute to the “greater good”.