Those on the left support radical or revolutionary change to society and social order, whereas those on the right support gradual change within the current system, if any change.
That's wrong in so many ways.
It doesn't make sense for certain elements of the Far-right, such as the Nazis, though I would tend to view that as an academic issue anyway. When we're talking about bad people, who cares what brand of bad they are?
The modern left in Western countries generally supports the opposite of "radical or revolutionary changes".
If they support the extant order of society, as you posit, then they are obviously not left-wing in any meaningful sense.
Would you call Russian communists circa 1992 left or right wing? On the one hand they are hard core socialists. On the other hand, they were supporting the status quo.
