Hey that’s an entire nest for that dove!

Being a pigeon dove, (probably a West Peruvian Dove by location) it’s probably looking for a hazardous place to put down the stick and lay an egg on it.

At what point does a twig become a stick? Are all twigs also sticks?

I feel like the difference between twig and stick must be not intrinsic to the stick, but a property of the observer. To a bird, a twig is already a stick, and to a giant, that which we call a stick is surely nothing but a mere twig.