An ADI is an Approved Driving Instructor DSA(link), they should display the green octagonal badge on the windscreen of their tuition vehicle.They are fully qualified & have so proved to be able to give tuition in the class of vehicle shown on the badge!

A PDI(Prospective Driving Instructor) is a trainee instructor they should display a pink triangular badge, a trainee instructor hasn't passed the final ADI exam, but is licenced to provide driving lessons, they are NOT fully qualified