Liz Buchanan BVSc MRCVS
Scenario two is where the puppy is not at all nervous of the big dog - quite the opposite - and barking to try and convince them to play. The posture accompanying this sort of approach is characterized by having the front end low to the ground, paws out front, and the bum in the air, tail raised and maybe even wagging. When my pup did this to the older dog, more often than not he would be completely ignored because the older dog just didn't have the same capacity to play. He could, however, continue to try to persuade her.
There are potentially other scenarios I could think of, but these two appear most commonly. Remember that in general, dogs have evolved a fantastic range of body-language to sort out any case of conflict or need for communication that may arise. Usually, even in scenario one, they will 'sort out' any conflict of interests for themselves without hurting one another. However, always keep an eye on them; they may not have chosen to live as a pack and this can take some adapting to. There is some suggestion that dogs who look completely different from one another (e.g. shepherd and pug) struggle to interpret one another's facial expressions, and that wolf-like faces are easier for dogs to read than pug-like faces. However, I am unsure what the evidence is for this. Perhaps if you could film the encounters e.g. on a smart-phone and show them to your vet, the vet will be able to give you some advice specific to the animals involved.