Turn signal doesn't blink: What's likely wrong?

It’s the flasher.

The flasher is not a relay. Can’t say I’ve ever heard of a turn signal relay, but if there is such a thing, it’s not a common design feature.

The hazards use a separate flasher then? I did not know that.

Depends on the car. Some designs use two separate flashers, some operate the turn signal and hazard lights through one flasher.