In most countries, I think both rights are managed by a single collective management society, but not in all. A collective management society's role is to represent all the owners of similar rights, but it is also to make an extensive repertoire of works available to users. A collective management society connects rights owners with groups of users. If, for example, a tariff is imposed on the music played in a restaurant, it will be imposed on all restaurant owners, collectively, and not on each one individually. What it does is allow for a much more efficient management process.
On May 5th, 2016. See this statement in context.