You just described a somewhat progressive leaning liberal.

There is, indeed, a lot of overlap, but, imo, the differences usually tend to revolve around one’s mentality — how they rationalize their arguments.

Those are about as anti libertarian as it gets, because they take away a lot of “individual” freedom

You are half right — universal healthcare isn’t classically liberatarian because it is an example of positive liberty, whereas libertarianism tends to align more with negative liberty.