Left = Egalitarian flat power structure https://en.wikipedia.org/wiki/Left-wing_politics

Right = Hierarchical power structure https://en.m.wikipedia.org/wiki/Right-wing_politics

The collectivist/individualist framework you describe is propaganda to appeal to supporters.

Authoritarianism is the sole perview of the right. What makes it confusing is that right wing people claim to support leftist ideals.