At 10am, you say to your sister: "I am going to see my friend at 8pm this evening" [you have planned this] At 7.45pm, your sister asks you to help her with something. You say: "Sorry, I can't help you - I am (just) about to see my friend." [You will shortly execute your plan]

It's a question of timescale. If you are about to do something, you are on the point of doing it. You are preparing to this IN THE NEXT FEW MOMENTS. If you are going to do something, this is a plan or intention, with no idea of timescale. For example, you can say 'I'm going to retire in 2018'. This is a plan, but it's a long way in the future. You use 'going to' for ANY time in the future - near or far.