A muttafaq ʿalayh report is, in common technical usage, one transmitted by both compilers in their Sahih collections. By contrast, ʿala shart al-shaykhayn refers to a report elsewhere whose narrators and remaining authenticity conditions match the standards associated with both compilers; the actual wording need not occur in either collection.
Distinction: “Recorded in both Sahih collections” is a bibliographic claim; “meets both compilers’ conditions” is a technical judgment requiring evidence.
Merely matching a list of narrator names is insufficient. Continuity, precision, freedom from disqualifying contradiction, and hidden defects still need examination.