Noise jammers don't transmit pulses, they transmit a continuous signal. There's no pulses you can filter.

A jammer that transmits a pulse based on the radar pulse is a deception jammer. It's used to create a false target. You already know this.

If the jammer emits pulses when the radar pulse hits it, and then slowly introduces a time delay pulse by pulse, it'll look like the target split in two. The real aircraft in front, and the fake jammer target behind.

If the radar uses a fixed PRF, then the jammer will know when the next pulse will arrive before it arrives, and so can transmit a jamming pulse before the radar pulse arrives. This also makes the target seem like it's split in two, but this time the closest target is the fake.

A radar can use jittering, where it varies it's PRF slightly pulse to pulse. This means the jammer will never know exactly when the next radar pulse will arrive, so can only produce fake targets behind the jammer, by starting a timer based on when the pulse arrives.

I think what you mean by PRF filtering, is a radar that uses jittering, and will only see targets which match the transmitted varying PRF.

Noise jamming just transmits a very powerful wall of noise, that covers the reflected signal, so range cannot be determined.

I should probably say I'm not an expert, so don't take what I say as law.