The presence of Gram-negative diplococci in sputum is characteristic of Moraxella catarrhalis, a common cause of respiratory tract infections especially in patients with chronic lung disease. Unlike Streptococcus pneumoniae, which appears as Gram-positive lancet-shaped diplococci, Moraxella is distinctly Gram-negative. Staphylococcus aureus and Pseudomonas aeruginosa present as Gram-positive cocci and Gram-negative rods respectively, not diplococci. Thus, identifying Gram-negative diplococci in sputum strongly suggests Moraxella catarrhalis infection.

Reference: Mandell, Douglas, and Bennett's Principles and Practice of Infectious Diseases, 9th Edition.