A proper limiter is a special case of a compressor, where the compression ratio is very high – set a threshold, and when signal’s volume goes over the threshold, reduce the volume by some ratio. If the ratio is inf:1 (in SC Compander terms, slopeAbove = 0), then the output signal can’t be louder than the threshold – that’s a limiter. (In practice, many audio engineering books say that a compression ratio > 10:1 is practically a limiter.)
All dynamics processors have attack (clamp) and release times. If you always instantaneously adjust the output level, the audio-rate amplitude modulation will distort the spectrum. I’d be skeptical of any compressor/limiter where the release time is shorter than 30 ms or so.
If there is no attack/release time, then it’s not a limiter.
tanh nor hard clipping have an attack or release. (They are really transfer functions for waveshaping.)