The Difference Between muttafaq ʿalayh and rawāhu al-Bukhārī wa Muslim
Introduction
The terms muttafaq ʿalayh and rawāhu al-Bukhārī wa Muslim are often used interchangeably, since both signal that a ḥadīth is recorded in both Imām al-Bukhārī's and Imām Muslim's collections. There is, however, a distinction between them, and it can be drawn out with two examples.
Example 1: can be termed muttafaq ʿalayh
The following ḥadīth is narrated in both Ṣaḥīḥ al-Bukhārī and Ṣaḥīḥ Muslim:
In both books the narrator is Abū Hurayrah (raḍ. ʿanhu). Because the same Companion is the source in both collections, the report qualifies as muttafaq ʿalayh: the agreement is not only in the matn but also in the chain at the level of the Companion.
Example 2: should not be termed muttafaq ʿalayh
The following ḥadīth is also recorded in both Ṣaḥīḥ al-Bukhārī and Ṣaḥīḥ Muslim, but with different narrators:
In Ṣaḥīḥ al-Bukhārī this ḥadīth is narrated by Jābir ibn ʿAbd Allāh (raḍ. ʿanhu); in Ṣaḥīḥ Muslim it is narrated by Ḥudhayfah and Abū Shaybah (raḍ. ʿanhumā). The wording is the same, but the Companion-level narrators differ, and so the more accurate label is rawāhu al-Bukhārī wa Muslim, "narrated by al-Bukhārī and Muslim", rather than muttafaq ʿalayh.
Conclusion
In short, muttafaq ʿalayh presupposes agreement at the level of the narrator as well as the matn. Where only the matn is shared and the chains diverge, the formula rawāhu al-Bukhārī wa Muslim is more precise.