Quoting the dictionary is incorrect when using these terms in the car industry.
Car valeting is the process of cleaning, polishing and waxing an auto-mobile in order to achieve an as-new look. this including waxing and polishing.
car polish is a product that uses an abrasive action to remove very fine layers of the top coat protection to flatten out the surface to ensure and equal reflection of the light and thus a highly polished look.
Wax is usually a natural product like bee's wax , virtually insoluble in water, so won’t immediately disappear after each wash or rain shower, used protect the car paint work.
Therefore by just applying your polish it wont add protection to the polished paintwork, which is where your wax comes in to protect all the hard work you have just put in polishing and a achieving that deep gloss shine. so you should polish then wax.