A cocktail whisk has a head that is small enough to be used in a bar glass and a handle that is long enough to reach the bottom of a tall glass.
Cocktail whisks do not have one predetermined head style. The core use of a bar whisk is to stir drinks in a glass or shaker.
This means that size, not design, determines what is and isn't a cocktail whisk.
It makes sense that these are often referred to as mini whisks.
Let's compare some common ones to their larger versions...
Here is what the flat bottom "mini" bar whisk looks like next to it's larger standard version Triangle Whisk
Here is what the balloon "mini" bar whisk looks like next to it's larger standard version Balloon Whisk
There are many different designs for the whisk head, but when they fit in a glass and can mix a drink, they are all cocktail whisks.
The easiest thing to get wrong about this type of whisk is the size.
If you are looking for a cocktail whisk, make sure the description mentions specifically that it is a bar, mini or cocktail type of whisk.
This is the tool we featured on this page in many of the images. Stainless steel - 9 inches - Mini Bar Whip.
This tool is also on this page in many of the images. Stainless steel - Mini Cocktail Whisk - 8.25 inches long.