Shopping cart is a North American name for the basket on wheels on can use to hold food while grocery shopping. Interestingly, it is not listed in some American dictionaries, but is listed in European.
In British English this item is more often called a shopping trolley.
Both versions of this term can be shortened to simply cart and trolley.
A buggy is a carriage or small wagon pulled by a horse. It can also be another term for the cart one uses to shop. This term is mainly spoken and understood in the Southern United States. Be aware, however, that this can also be a term for a child’s stroller or pushchair and can be extremely confusing to some audiences.
There are several other names used in English-speaking countries. They are usually regionally specific and not as widespread as shopping cart and shopping trolley.
Note that the term shopping cart is also the name of the portion of a website where one’s purchases are stored before one checks out and orders the items.
Examples
Inventor Sylvan Goldman’s prototype for the shopping cart was nothing more than two wire baskets attached to a folding chair, but it was the start of what would become a supermarket staple. [CNN]
They have also devised some bizarre flavours – from gin & tonic to cheese on toast – to tempt us to throw them in the shopping trolley. [The Telegraph]
I was looking for my car with a buggy full of groceries. [Forth Worth Star Telegram]