What is the consensus in the scientific community over COVID-19's mode of transmission?
The terminology really depends on the scientific field. You also have to be aware that sometimes terminology is simplified for the purposes of presenting information to the general public.
A droplet can really mean anything from a few micrometers up to several millimeters and it does not necessarily have to be spherical. The key point is that the virus may spread through droplets.
Aerosols typically refer to small solid particles or liquid droplets, maybe less than 20 micrometer in size, but again, it depends on the field.
In quiescent air, any heavy (more dense than air) particulates (solid or liquid) which are about 1 micrometer  or less will remain suspended in the air for several hours due to Brownian motion and also the fact that their gravitational settling velocity is small.