[new2this]

This description matches my experience interacting with multiple COO's at startups of varying size. Most CEO's I know look outwards and to the future, the COO ensures the company executes against the path the CEO has set

The role responsibilities are nebulous and change based on the company, but can generally be described as "whatever is necessary for the business to run". That could mean they focus on running Sales, Marketing, Support, Customer Success, but they could also oversee Operations and in some cases Product.