"Buggy" originated with the McLaren Baby Buggy in the mid-70s, which was the first truly portable pushchair and folded rather like an umbrella. It was very light to carry and easy to operate, but a bit basic (and probably uncomfortable!) Since then, the word 'buggy' has been used to denote any lightweight folding pushchair.
In the USA the same thing is called a 'stroller.'
Here endeth the lesson!