How are "One-Way" and "Two-Way" insurance understood in Quebec?

These are colloquial terms, not official terminology.

One-Way (Third-Party Liability):
Usually refers to purchasing only the legally mandatory Third-Party Liability (Civil Liability) insurance.
This coverage primarily pays for property damage to others, with a statutory minimum coverage typically quite high (e.g., 2 million CAD).
If you injure someone while driving outside Quebec (e.g., in Ontario or the US), this coverage applies.

Special case:
In Quebec, if you have only "One-Way" insurance and are completely not at fault in an accident and the other party can be found, your insurance company will typically cover your vehicle damage.

Two-Way (Full Coverage):
Usually refers to having Third-Party Liability insurance plus coverage for your own vehicle damage, primarily including Collision and Comprehensive coverage.