Places that serve cuisine of a single country or a region can be classified as single cuisine restaurants. They may be fine dining kind or a casual one. Like restaurants serving Indian food only will come under this category or only French or only Italian or only Chinese and so on.
Then there are restaurants serving food of different countries or regions. They will fall into the category of multi cuisine restaurants. Again they may be fine dining or casual dining restaurants.
The specialty restaurants are those which serve only a specific kind of food. It may be a tikka junction serving only tikkas of all kinds, it may be a chaat junction serving variety of chaat or you can say only pizzas or only Burgers or only Kathi rolls etc. Thus they specialize in one kind of food of any cuisine.
There is few difference between global restaurant and multi cuisine restaurant. One of difference is that global restaurant have signature dishes ex. KFC have chicken lollipop and Dominoz have its amazing pizza. But Top Multi Cuisine Restaurants have all type of foods and they make all kind of dishes. You can check that they recently added some new food culture.