If you ignore the American political spectrum for a hot minute and get down to the core of it, a practical definition of "left" and "right" is "no hierarchy" vs "hierarchy". This holds true in economics as well as social issues:
Racism is a system of hierarchy where one race is inherently good and normal and others are deviations from that, or at least every race is good or bad in some ways and there is an implied value judgement in every assertion about them. Not every person doing a racism necessarily fully commits to racial pseudoscience but if pressed they'll have to justify their conceptions by citing them. Racial mixing of course is unacceptable as it goes against this order and since the racial social castes are a natural order, any attempt to overcome them is bad and anyone making it further than their kind is expected to should either be celebrated for their excellence (and everyone else be held to their standard to demonstrate their insufficiency) or be viewed with suspicion because they probably cheated or got handouts.
Sexism is a sexual hierarchy with women being one way, men another and everyone who doesn't neatly fit into either category being deviant and a troublemaker. It's not so much about one sex being better at all things than the other, much like racism, but about there being a natural order and everything being well as long as people follow it.
Economic right wing thought posits that there is a natural order in that poverty is largely a failure of the individual and can be overcome with sheer will so wealth is the just spoils of success and personal quality and charity is the only acceptable form of welfare because it is for the wealthy to decide how to allocate their deserved riches.
This is also why right-wing people have recently picked up the term "Marxist" (or even "Neomarxist") to describe not just socialists but also progressives in general, even when they lean economically more right-wing than left.
The question of how you align within that spectrum is mostly a question of whether you think a natural order exists and/or should be enforced in each of these dimensions (and there are probably more). Most Democrats don't want to abolish private ownership, they just want more regulations to shift some of the wealth to the lower classes, i.e. balance out the hierarchy rather than getting rid of it. They are however more likely to be opposed to the idea of a natural order in social questions.