indeed there are many find that dog, or find that breed, but
find that dog: fina a dog, purebred or mutt, doing something
find that show dog: find a dog in stack position, like in a show
find the puppy: find a puppy doing something or in a specific place or with an animal companion
find that litter: find a litter with mom and all of certain breed
etc.

each has its own specifics, but some people (i wanna think) get confused and post puppies in adults, adults in puppies, headshot instead of stacked, etc