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The clinical feature that differentiates septic arthritis from a pyogenic infection is the rapid onset of monoarthritis. Septic arthritis is often characterized by a quick onset, with patients typically presenting with severe unilateral joint pain and swelling, usually affecting a single joint, hence the term "monoarthritis." This rapid onset can be attributed to the acute inflammatory response triggered by the introduction of pathogens into the joint space, leading to swift deterioration and symptom expression.

In contrast, a pyogenic infection may not always present with the same rapidity or specificity in terms of joint involvement. Pyogenic infections can appear more gradually, involve multiple joints (polyarthritis), or present with systemic symptoms that are less acute than those seen in septic arthritis. Hence, the immediacy and singularity of the joint involvement in septic arthritis serve as distinguishing features from more generalized pyogenic infections.

The other clinical features mentioned, such as fever and localized redness and warmth, can also be observed in both conditions and do not sufficiently distinguish between them. Elevated alkaline phosphatase levels are more indicative of bone or liver pathology rather than providing a clear distinction between septic arthritis and a pyogenic infection.