But as far as we know, the bare virus does not travel through the air, it only travels in droplets. Although there is some disagreement on how large those droplets are.

I feel like I have a wrong model of how things work.

I'm thinking that for each virus there is a chance that it will infect a cell. The higher the viral load, the higher the number of chances that you will get infected.

a lower number of droplets -> lower viral load -> less chance to be infected.

What is the physical explanation behind this fact, and how come normal masks protect others if a carrier wears it?

The physical explanation is simple, the gaps between the strings of the mask are significantly wider than 50-100 nm. The mask protects others through preventing you from breathing/coughing on them, which it does way better than preventing you from breathing contaminated particles in.

so you're saying that the gaps are so wide that almost no contaminated particle (getting in) will get stuck on the mask?

but somehow (some of the) particles going out will get stuck.

how is that simple?