A drone operator is any person, whether natural or an
organisation, who owns the drone(s) or rents the drone. You can be both a
drone operator and a remote pilot if you are also the person who actually flies the
drone. However, you could be the remote pilot without being a drone operator, if,
for example, you are a pilot working for a company which provides services with
drones. In that case, the company is the drone operator and you are the remote
pilot.
If you bought a drone to fly it in your leisure time, you are both the drone operator
and remote pilot.
If you bought a drone to give away as a gift, the person who will receive the gift and
then fly the drone will be the drone operator and the remote pilot.

(Reference Source EASA's FAQS)