a) you were never, or are not, a child.
b) read on, MacDuff
The best way to think of a train set is to imagine a little train (which more often than not looks nothing like a real one), perhaps on a track, with a child pushing it round the living room floor making extremely irritating "Whoo Whoo!" and "Chuff Chuff Chuff" noises. Almost anyone you know, at some point, will have owned a train set in childhood. Inevitably, the original train set will get bigger and more complex, maybe getting to the point where the owner will start making, buying or bugging the parent for, scenery. If this happens, it is almost a sure sign that it will, one day, probably overnight, even, make the magical transformation into a Model Railway. This is merely an advanced train set, on which the owner runs, crashes, and gets mad with, his/her train(s). Usually this is either to a strict timetable, or just running trains at random. It involves change for the owner, too. It can transform any normal, sane, person into a single-minded one-tracked train fanatic. This can cause frenzies of strange, elusive crafts, practised only by modellers, such as "super-detailing" and "fixing" (this is not to be confused with repairing, which involves duct tape, something which most modellers loath and detest). Never EVER confuse a train set with a model railway, train sets are primitive in comparison. Model railways can be anything from exact scale models of, say, Kings Cross, to models of an imaginary station.
Every now and again, the common railway modeller may throw a kit of a model train across the room after changing one of the components beynd repair and then realising that it was merely upside down, while the wife (daughter, girlfriend, resident alien etc.) says that she/he/it thought it was meant to be a relaxing hobby.
The main difference between model railways and train sets is the price. If you could pick it up for under £20 at a jumble sale, it's a train set. If it costs £80+ it's a model railway. Another, secondary difference is called "detail". Model Railways are generally (note generally!) more detailed than the average, say, Brio (TM) wooden train set.
For more detail, see the guide entry titled "Model Railways", incidently, by the same author before THEY changed my login details, deleted my account, or I forgot my details.
If you know someone who is acting strangely, before you report them to the looney bin, ask if they are a railway modeller. I know, speaking from past experience, and being one from 8 years old.
And whisper it who may, but at the end of the day we are just playing trains, aren't we?