Is there a difference between "counting" and "determining relative size"? for example, I can distinguish between a group of three people and a group of ten peop

Is there a difference between "counting" and "determining relative size"? for example, I can distinguish between a group of three people and a group of ten people without being able to count at all. There are big differences in the amount of noise, motion, smell, etc that don't require a concept of numbers. I feel like the author uses several examples that are based on relative size, and also examples that appear to require actual counting (ie the cowbirds at the end). It kind of muddies the issue, but overall interesting ideas