This isn’t really accurate. Socialism is the domination of the proletariat over the bourgeoisie, ie worker ownership of the Means of Production, and the path towards Communism, an eventual stateless, classless, moneyless society.
Are you familiar with Communist theory? Equity isn’t the goal, fulfilling everyone’s needs is.
I consider myself a socialist/leftist and my primary concern right now is not to dominate the bourgeoisie. It’s mainly to get them to stop tax evasion so we can fund our public schools and hospitals. And if they could stop voting for candidates who are in coalition with the far right that’d be nice too!
That’s Social Democracy, ie what the Nordic Countries are, not Socialism and not Leftism.
Oh boy I’m no social democrat. A radical socialist if you prefer. You can have radical ideas like ending capitalism or taxing inheritance to 100% while still being for democracy and not being a revolutionary.