The term originates from a Poodle trim. The "Puppy Cut" is a trim used on a Poodle under 12 months to prep their coat for the mature show dog trims with poms, bracelets, and jacket. 

In pet grooming, these  terms are generalized terms for "the same length all over the body". Moreover, the better term for this cut would be the Poodle's "Kennel Cut". 

A type of Poodle cut. This cut has a shorter body and longer legs with/without the shaved face and feet.  

A modification of the Lamb Cut which brings the short body cut down to the elbows and down the rear of the dog with a stylized head to balance the body. 

The front is clipped shorter to the elbows, but the rear is left higher to give it a rounded appearance. The Teddy Bear cut also has a rounded head and short ears to give the 🧸🐻🧸 look.