Buggies & Strollers / “umbrella stroller”. This stroller is used for toddlers. And when folded takes on the look of an umbrella with the curved hook at the top. That can be hung in most places or on your arm. It is very lightweight and portable.
A buggy, by the definition you found, would also sound to be what Americans call a folding stroller. Like the pushchair it faces the passenger outward and has them seated. But is built like a typical lawn chair, of metal tubing and fabric stretched between to form the seat and back.
Also known as, a light folding chair on wheels, in which a baby or young child can be pushed along.