A Rose by Any Other Name Still Has Thorns

A long time ago, during an internet argument, I coined the phrase "state capitalism" to describe what they are currently doing in Red China. My argument was that all economic systems are capitalist, the only difference being who controls the capital. Capital is defined as money or goods that are used to generate more money or goods instead of being used for immediate consumption. I argued that even a hunter-gatherer economy is capitalistic, with Mother Nature being the capitalist. That's because, if our hunter gatherers consumed all the resources at their disposal instead of leaving some for seed, they would have to move around a lot, which I guess they did. If they return to the same territory someday, they will likely find that the resources have recovered in their absence, unless another band of greedy consumers has gotten there first and used everything up again.

Socialism is harder to define because, as you say, it seems to mean different things to different people. Generally, I would say that it's a system where the government confiscates and redistributes wealth. By that definition, all governments are socialistic by their very nature, varying only in degree. Canada is probably more socialistic than the U.S., and I understand that Sweden is even more that way. Russia used to be even more socialist than Sweden, but I don't think they are anymore. China is currently one of the most socialistic countries in the world, but they may be drifting away from that position. It's hard to tell with those guys because they, like most Orientals, are inscrutable. The movement towards socialism in the Western democracies has been evolutionary, not revolutionary, which is why some people call it "creeping socialism". It has mostly been achieved by democratic means, which is why some people call it "democratic socialism".

Comparing communism or socialism to democracy is indeed like comparing apples to oranges.
Democracy is not a system of economics, it has to do with how the political leadership is chosen. It's not even a form of government, because you can have a democratic monarchy or a democratic republic. It just means that whatever form of leadership you have is chosen by popular vote. Universal suffrage is a fairly new concept, and has not yet been fully implemented anywhere that I know of.  No democracy in history has allowed all their people to vote. We currently allow a greater percentage of our population to vote than we ever have, which is why I said that we are more democratic than we've ever been.

I'm not sure how all this applies to the rich getting richer and the poor getting poorer. If you attempt to close that gap by confiscation and redistribution of wealth, you are just reducing everybody to the lowest common denominator. That might seem fair to the guys on the bottom, but the guys on the top are certain to resist it. A better plan would be to let the rich people keep their money and provide a means for the poor people to get some of their own. It's not a zero sum game because the Federal Reserve is cranking out new money all the time. Just find a way for some of that new money to get into the hands of the poor people and leave the old money alone.