I’m not going to get into the political definitions of socialism and communism, but from a strictly economic point of view, I don’t consider communism to be a separate economic philosophy from socialism. Instead, I would opt to characterize socialism and capitalism as two ends of a spectrum. On this spectrum, socialism is a system where the government controls all aspects of the economy and capitalism is a system where government controls no aspects of the economy. Every economy in the real world, then, falls somewhere along this spectrum.
So, we can talk about whether two economies are more socialist or capitalist relative to each other, or we can talk about whether specific sectors of an economy are more socialist or capitalist. So, for example, I would characterize Norway overall as being more socialist than the US. But within the US, I could say that we have multiple systems of socialist health insurance (Medicare and Medicaid) and we have multiple systems of capitalist health insurance.
I don’t consider regulation per-se to be indicative of either system, although you can certainly set up regulatory systems that tilt one way or the other. And I also realize that many people would characterize something like Medicare to be wealth redistribution, rather than socialism, but I consider wealth redistribution to be government control of the economy, so wealth redistribution (in my view) would push towards the socialist side.
Now, the reason I separated out the economics, is because you can have a wide variety of economic systems with government systems. So, for example, I would characterize the USSR as having a highly-socialized totalitarian system, while I would characterize the UK as having a somewhat-socialized democratic system. Although, I do feel that as you get close and closer to either end of the spectrum, it becomes more and more difficult to maintain democratic forms of government.
ETA: A number of people probably won’t agree with the way I’m defining socialism, capitalism, and wealth redistribution, so whatever terms you want to substitute, feel free. The distinction I’m trying to make is between government control and non-government control.