Socialism is socialism, right? It's not communism.
Socialism
https://education.yahoo.com/reference/dictionary/entry/socialism
"Any of various theories or systems of social organization in which the means of producing and distributing goods is owned collectively or by a centralized government that often plans and controls the economy.
The stage in Marxist-Leninist theory intermediate between capitalism and communism, in which collective ownership of the economy under the dictatorship of the proletariat has not yet been successfully achieved."
So, it's the controlling of business by the government. You could claim that the NHS and things like this are socialism, I wouldn't necessarily agree, but you could claim it.
Communism
https://education.yahoo.com/reference/dictionary/entry/communism
"A theoretical economic system characterized by the collective ownership of property and by the organization of labor for the common advantage of all members.
Communism
A system of government in which the state plans and controls the economy and a single, often authoritarian party holds power, claiming to make progress toward a higher social order in which all goods are equally shared by the people.
The Marxist-Leninist version of Communist doctrine that advocates the overthrow of capitalism by the revolution of the proletariat."
Communism goes much further, it's ownership of business not just by the govt, but by collectives, in theory (which has basically never really been reality) this means the people are in charge, not the govt.
So, Communism in the sense of the healthcare system would be that all people, somehow, participate, which I'm not sure I can actually visualize how it might work. Would all workers have to learn how to be doctors? Or would some doctors merely work as doctors and get paid the same as others? I don't know.
People equate this to Communism because they've had it drilled into their heads since 1945 that this is the case. Nothing more really. Ask those who hate Communism why they hate it, and they might be able to come up with some propaganda they got told, but they'd struggle to tell you what Communism actually means.