What distinguishes “muttafaq ʿalayh” from “ʿala shart al-shaykhayn”?

Comparing the Two Sahih Collections and Ranking Sound Reports

• The first denotes inclusion in both collections; the second asserts satisfaction of both compilers’ criteria
• Meeting both conditions necessarily proves inclusion in both books
• Muttafaq ʿalayh means only that the same narrator occurs somewhere in both books
• Matching both conditions removes the need to check anomalies and hidden defects