Whilst learning to drive you will come across different people and organisations. Here's a short list.....
Driving Standards Agency (DSA)
The Driving Standards Agency are the people who set the standards, approve and test driving instructors, handle all test applications, produce official training materials, and their examiners will take you for your driving test.
Driver and Vehicle Licensing Agency (DVLA)
The Driver and Vehicle Licensing Agency are the people who handle licence applications, vehicle registration, road tax, medical conditions, personalised registration plates and any endorsements (points on your licence) or disqualifications.
Approved Driving Instructors and Trainee Driving Instructors (ADI / PDI)
ADI means an Approved Driving Instructor, they should display the green octagon badge on the windscreen of their training car. PDI means that the instructor is a trainee they should display a pink triangle badge, a trainee instructor hasn't passed the final ADI exam, but is licenced to provide driving lessons.