In the way the words are being used here, it absolutely does.

There's been a lot of propaganda for a long time that "socialist" countries are authoritarian, abusive, and usually dictatorships, so by that measure, of course you would have to make the argument you do, but the fact of the matter is that socialist policies are just policies where we pool resources as a group to provide a public good. It's opposite would actually be free market capitalism, where you have to subscribe to a fire service to protect your house (it worked that way on the US once, feel free to Google it).

The methods of governing are a completely separate axis, ranging between power vested solely in an individual or small group, and true democracy.

It is absolutely possible to have countries that are democratically socialist, or free market dictatorships. Just because America is still mainly a democracy doesn't mean we can't look at it's policies and see a clearly socialist component of public services. In my mind the truly perplexing thing is how people can label things like a tax to provide everyone access to free books and other media, taxes that support universal fire and police protection, and taxes that support free education for everyone (through high school only!) and say they are just normal non-socialist things, and then look at taxes that would pay for higher level education, for health protection, or for childcare so you are always able to go earn a living, and suddenly they are foaming at the mouth and screaming "socialism!"

But trying to derail an entire conversation by arguing about one word is a lot easier than trying to actually address the points of an argument, so we see that a lot.