The issue is that droplet transmission starts out airborne, in the sense that the person expells the saliva with the pathogen into the air, but then those droplets settle on surfaces. Droplets are too heavy to remain airborne and thus once they settle you pick them up by touching the surface they landed on, then rubbing your eye, nose, or other mucous membrane. This is why droplet transmission is still considered a form of person-to-person transmission; it is essentially spitting on someone, but with a surface (or fomite) between the two people.
This is why masks are not the only way to prevent droplet transmission - I can be wearing a mask, but then enter a room that someone sneezed in 4 hours earlier, touch the keyboard they sneezed on, rub my eye, and then get infected.
(Used to teach a course on infection control -- made several students compulsive hand-washers!
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