As far as I know there is no legal definition of convenience retailing. When this magazine first got cracking 21 years ago as the first in a new sector, we often puzzled over the definition. We came up with a business under 3,000 sq ft with a marketing mix of grocery, chilled, fresh fruit & veg, snacks and soft drinks, off licence, newspapers and magazines, and takeaway food.
There was also that indefinable extra - a bright shiny, slightly Americanised store that reflected a modern 'can-do' approach to retail. Meanwhile, the supers continued to be called 'grocers' and when, in 1985, a High Court case tested the term 'grocery' and 'provisions' used in a lease, it decided that a convenience or corner shop whose lease says 'grocery' can sell any of the lines that those proper grocers (Sainsbury's, Tesco et al) sell in their stores unless there were specific restrictions mentioned. So with a description of 'grocery' in your lease, I reckon the sky's the limit.
I wouldn't want to be saddled with the description of 'greengrocer', although one day, what with climate change and ecological pressures, I shouldn't be surprised if Sainsbury - and certainly Waitrose - market themselves under such a banner.