Question: how many different types of engineers are there

Good question. In the UK there are professional institutions covering most disciplines. When I looked a couple of years ago the following disciplines were mentioned: Acoustic – Aeronautical – Agricultural – Bio-Medical – Building Services – Cast Metals – Chemical – Civil – Electrical – Electronic – Energy – Design – Environmental – Fire – Gas – Healthcare – Highways – Transportation – Information Technology – Lighting – Marine – Materials, Minerals & Mining – Measurement & Control – Mechanical – Metallurgy – Military – Naval Architecture – Non-Destructive Testing – Nuclear – Operations – Physics & Medicine – Plumbing & Heating – Railway Signalling – Robotics – Structural – Tribology – Water – Welding. But whatever discipline one initially trains in, there is always a need to understand how, where and why the other disciplines will interface/interact with your own. I am a Marine and Mechanical engineer, but every project that I have dealt with required elements of Civil engineering, Electrical engineering, Control engineering, and others. Even within discipline areas there are finer divisions. Transportation could refer to trains, lorries, vans, cars, F1 racing cars, etc. There is something for everyone.