Yes, cart=buggy.

Actually, the PGA Tour mandates no cart for any reason - infirm or not.

A couple years back, there was this fellow with a (pardon the expression) bum leg. He could golf well, but it was a struggle for him to walk. SO when he played, he rode. Posted some fine scores. Was on some mini tour when the controversy came up - he rides, they walk. To 'protect the field', either everyone walks, or everyone rides.