The question really should be asked if there is anything like a cocktail coffee table or not. Shouldn’t it have been a cocktail table as a standalone table or a coffee table also as a standalone table? If you are thinking of something right now on this, it should not be far from if there is really any difference between a cocktail table or a coffee table at all.
What you use the table for defines it
A cocktail and a coffee are both foods of their own. So, one may define the table based on the use of the table. That is, if you have a table with a cocktail, it becomes a cocktail table and if you have a coffee, it becomes a coffee table. In all, that general center table is a coffee table that can also be a cocktail table. To call it a cocktail coffee table can just be for the common use of the language. It is better called a cocktail table or a coffee table.
In as much both can mean the same table, it is widely acclaimed that a cocktail table and a coffee table has some difference in the design pattern.
A cocktail table
A cocktail table is believed to be that conventional small rectangular or square shaped center table. These shapes are the convention for a cocktail table. This is just how some people differentiate it from a coffee table.
A coffee table
A coffee table is that sleek and stylish round or oval design of the living room center table. Both the cocktail and the coffee table function in a similar way in the living room. It may be difficult at times to separate one from the other. Probably what you will find in many homes today would be the coffee table because it seems modern in the finishes you will find, for instance, a glass top and some cool metal designs.
Whichever the design you choose to go for, calling it a cocktail coffee table will still make some sense for what you mean in the use of the table.