Depends on the limiter.

Hard limiters limit by clipping.

If you look at the output waveform, I mean. It’s why limiters are sometimes used for distortion. The flat top and/or bottom create overtones.

I get that terms get overloaded especially when mixing between electronics, signal processing, and commercial products. But in the context of audio signal processing that would not be called a "limiter" - it's a clipper or clamper. You won't see products advertised as a "hard" or "soft" limiter - but you will see "hard clipper" or "soft clipper" used to describe that behavior.

The distinction is that limiters and other dynamic range processors do not use clipper circuits/algorithms directly, they have an amplifier controlled by a feedback or feedforward signal path as the gain computer. The amplifier may create harmonic distortion, or harmonic distortion can be created if an envelope follower in the feedback/forward path is configured in a certain way, but it isn't the design or intention of a limiter to clip.

Limiters can can clip if there's a clipper after the gain reduction which happens in some designs where the limiter is load bearing or uses a feedback path and no lookahead, but those are pretty rare these days since the entire point of a limiter is to avoid distortion.

A good book that covers the design and theory of operation is Zolzer's Digital Audio Signal Processing. It's relevant even for analog designs, since the topology of the designs are the same.