The political terms "left" and "right" come from the French revolution. The members of the the French Estates General who favored the monarchy, the Ancien Regime, tended to sit on the right side of the aisle, while those who opposed it sat on the left. Over the 19th Century, the "left" tended to become more and more associated with being open to change (such as socialism), etc. while the right wingers remained pretty much reactionary, resisting all change.

From far left to far right, at least as I was taught in high school in the early 19-ought-60s:

Radical: in favor change, no matter the cost to society.
Communist: socialism with no private property.
Socialist: the Gubmint's ownership the means of production and distribution (Amtrak and NEC are examples of this).
Liberal: more open to change than a moderate.
Moderate: a conservative open to some change, usually at a slow-ish rate.
Conservative: not open to change at all.
Reactionary: conservative who wants to turn back the clock "to the good ol' days of being able to exploit natural resources and employees and a restricted franchise (no female nor minority voting rights).

Not sure where anarchism fits in, unless you include places like central America.

I was raised to be an FDR hater. Since then I've discovered that this was too simplistic an outlook because while both the left and right have good ideas an policies, they also have bad ones.