Over the years, I have met with business owners who define their business as being a cafe...but NOT a Coffee Shop.
When I ask them what they mean by this, the answer is not precise, but for most, it seems that it has a lot to do with what is on the menu.
As the High Street coffee chains have developed over the past decade or so, there is a focus on barista led, hand made quality coffees as a speciality.
On the food side, there is a tendency (but not exclusively) to focus on sandwiches and cakes, which might include hot sandwich formats such as panini or toasties, but that is more or less it. While some High St. chains have recognised the demand for breakfast products, their solution is based around a heated up sausage/bacon sandwich.
None of the big chains offer plated hot meals, so a full English fried breakfast is not on offer. So, at one level at least a Cafe may be seen as an establishment which offers such.