What does a "measurement" actually mean in quantum physics? (Double-Slit Experiment)

Take the double-slit experiment with photons.

With no photon detectors on the slits, the photons get distributed as a wave.
With photon detectors on both slits, the photons get distributed as particles (two clumps).

Say the photon detectors get weaker and weaker photon detections as they get farther and farther away from the stream of photons, with individual detections from greater distances gradually blurring into background noise.

If the photon detectors are in another building, the photons get distributed as a wave, since you might as well assume the detectors aren't there at all.
If they are placed directly on the experiment, the photons get distributed as particles (two clumps).

What happens in the inbetween space? What happens to the results of the double-slit experiment when you gradually bring that particle detector closer to the slits?

Is there a tipping point where waves suddenly become particles, or does the photon distribution end up with some photons treated as a wave and some treated as a particle, or something else?