“If you can’t measure it, you can’t improve it.”
It is undeniably one of the most crucial parts of a Digital Marketing team and the half-brother of Search Engine Optimization.
Well, Paid Media Specialists focus on optimizing the paid search and all the display or social ads of a Digital Marketing Campaign, while the SEO's focus is more of the "Organic" approach side of things.
Other terms for Paid Media Specialist:
SEM - Search Engine Marketer
Paid Search Manager
But for the love of God don't use PMS as a short name for this one. ;)