Today, when looking up the definitions of the phrasal verb "take sth up", I noticed that one of them was written like this: "to start or begin something such as a job." For the first time I realised that probably "start" and "begin" don't exactly mean the same thing.So the question is what the difference is between the two, and if there are cases when they mean exactly the same thing.
In a great many contexts, to start and to begin are effectively synonyms, but there are plenty of contexts where they aren't.
You can only start your car (make the engine begin running). You can't begin the car.
A loud noise can only make you start (be startled)
You can start out on a journey (or just start, or begin, but not begin out on a journey)
Idiomatic "Don't [you] start!" (just keep out of this argument!) doesn't work with begin.
I'm sure there are many other cases I haven't included. But the general rule is that where the meaning is to commence, the two words are interchangeable (though in some contexts one might be more likely than the other).