If one wants to acquire intuition into quantum mechanics and how it is the lowest level of manifestation of matter/energy one has to accept the duality particle/wave.
The particle manifestation is a particle as we know it in the macrocosm in the sense of being localized in time and space within the Heisenberg Uncertainty Principle, because hbar is a very small number.
The wave manifestation is a probability wave, it is functionally a wave form but the value it gives is just the probability for the particle nature to manifest at that (x,y,z,t) coordinate.
Then, what makes matter waves to collapse into particles?
They do not really collapse because there are no matter waves, there are probability amplitudes for the existence of matter at the specific (x,y,z,t). The observation of a hit on a film or detector indicates the passing of a particle from that particular (x,y,z,t) coordinate, and an accumulation of such measurements displays a wave pattern for the probability of a particle to diffract through the slits.
Does the screen allow detection as particles because it is a different type of particles?
It is not the screen that allows the detection. The screen absorbs all particles which do not pass through the holes. It is the holes that have to be commensurate to hbar in order to be able to detect the quantum mechanical behavior.