Manufacturers, retailers, cooks and dictionary writers differ in their opinions on this question, but most people would accept the following:
A frying pan has sloping sides and is usually sold without a lid. The sloping sides help to prevent a build-up of steam in the pan.
A sauté pan generally has a lid and more-or-less vertical sides, so that the food can be shaken in the pan without spilling.
A skillet is another word for a frying pan. Some manufacturers may use the word to differentiate between two types of pan, but without any noticeable consistency.
An omelette pan has sides that are more flared than an ordinary frying pan to enable the omelette to slide easily out of the pan.
A griddle pan is usually defined as a flat, often cast iron, pan used for cooking things like flat bread and pancakes with dry heat or a minimum of oil. It may have one or two handles and either no sides or very low sides.
However, many manufacturers now use griddle pan to describe a pan with ridges on the bottom, often square in shape, used for cooking meat and fish.