All dogs/puppies are different when it comes to potty training. Like the Shih Tzu puppy you described, my Maltese pup Mac just never seemed to take to indoor potty training very well (i.e., paper training). He was crate trained and would potty on the papers in the litter box in his crate if he absolutely could not hold it any longer, but he never made the connection between going to the papers when he had to potty while inside the house. He does fine outside, however, and we are happy with it!

My new puppy, Mei, who is also a Shih Tzu, is beautifully paper trained....for potty, that is. She knows to go to the papers when she needs to potty, but she doesn't seem to make that same mental connection with poop....therefore, she's had quite a few accidents. However, she is only about 11 weeks old, and she is also learning to go outside, so in short.....I guess my advice would be to go with the flow, and cultivate what the pup seems best at!!