A Flyer ID and an Operator ID serve different purposes, and only one of them costs anything.
Flyer ID
Cost: free
Valid for: 5 years
The Flyer ID shows that you, as the remote pilot, have passed the CAA's online theory test. It is a free multiple choice test taken on the CAA website.
You need one if you fly a drone or model aircraft weighing 100g or more. The CAA recommends getting one for lighter aircraft too, but it is not compulsory. The minimum age is 13, and children under 13 must have a parent or guardian with them when they take the test.
Operator ID
Cost: an annual registration fee set by the CAA
Valid for: 1 year, renewed annually
The Operator ID is for the person or organisation responsible for the aircraft, rather than the person flying it. It must be labelled on your aircraft, and you use the same Operator ID for every drone you are responsible for.
You need one if your aircraft weighs 250g or more, or weighs 100g or more and has a camera. It is optional below those thresholds. The minimum age is 18, so a parent or guardian must register if a child owns an aircraft that needs one.
If you are responsible for aircraft but will not fly them yourself, you can register as an operator only, without a Flyer ID.
What does the Operator ID cost?
The CAA reviews its registration fee each year, so rather than quote a figure that goes out of date, please check the current cost on the CAA's own registration service:
