Step 1: Understanding the Concept:
Phenotypic and biochemical differentiation of Staphylococcus intermedius group (SIG) members from Staphylococcus aureus in veterinary clinical microbiology.
Step 2: Detailed Explanation:
Diagnostic biochemical profile of Staphylococcus pseudintermedius (the major pyogenic pathogen in canine pyoderma and otitis):
1. Coagulase Test: It is Coagulase-positive (clots rabbit/canine plasma), ruling out character A.
2. Polymyxin B Susceptibility (B): It is characteristically susceptible to polymyxin B ($300\text{ units}$ disc), differentiating it from polymyxin B-resistant S. aureus.
3. Voges-Proskauer Test (C): It is VP-negative (acetoin negative), whereas S. aureus is VP-positive.
4. $\beta$-Galactosidase Activity (D): It is ONPG positive (possesses $\beta$-galactosidase), unlike S. aureus which is ONPG negative.
Therefore, characters B and D accurately identify S. pseudintermedius.
Step 3: Final Answer:
Thus, the correct answer is B and D only, corresponding to option (A).