Mutawatir is when a narration gains a huge amount of narrators that it being a lie has basically become impossible, in other words there would basically be no doubt in regards to it's authenticity. But Tawtur has terms, and the terms have been split into Mutaffaq alaih/that which has been agreed upon, and Al Mukhtalaf Feeh/that which there is difference upon. So the question is, what are the terms that fall under Mutaffaq Alaih (متفق عليه) ? and what are those terms which fall under Mukhtalaf feeh (مختلف فيه) ?
As @jikolp quoted it seems that you misunderstood the statement mutafaqun 'alayhi متفق عليه (can be translated "in agreement about") only means that both al-Bukhari and Muslim have quoted a hadith in their sahih. As each of them has his own definition on what he calls sahih. And this doesn't exclude that the same hadith with the same matn (content) is quoted in any other hadith collection!
As you see this has nothing to do with tawator, as in both Sahih books you may also find ahadith ahaad! As tawator is not quantitative expression it is used to show that a hadith has been narrated by many/different sahaba via many/different tab'iyn and so on. While both sahihs include ahadith ahad which means ahadith which don't have any tawator and you might find some of them marked as mutafaqun 'alayhi!
Condition of al-Bukhari, Muslim the two sheikhs
Al-Bukhari and Muslim both had a number of scholars (narrator chains) whom they trusted and some of them are common for both of them and some only trusted by Muslim or only by al-Bukhari! Now any hadith quoted as متفق عليه or رواه الشيخان would also be quoted to be sahih according the conditions of both al-Bukhari and Muslim (according to the condition(s) of the two sheikhs) على شرط الشيخين. But for example if a scholar like al-Hakim who wrote his mustadrak as an expansion for both sahih according either the conditions of al Bukhari على شرط البخاري this my mean the narrator chain could be found in Sahih al-Bukhari or على شرط مسلم this my mean the narrator chain could be found in Sahih Muslim or على شرط الشيخين which is explained above: then this would mean that the mentioned hadith is not in any of the two books but the rawys have been quoted in the Sahih books but either one or both of them have not quoted the hadith!
Rawahu a-Sheikhan رواه الشيخان vs Mutafaq 'alaih متفق عليه
The difference between متفق عليه and رواه الشيخان generally is as follows:
- متفق عليه: means the hadith is mentioned in both sahih books with the same matn (content) and narrated by the same sahabi!
Note that the exact wording of the content could have slight differences.
- رواه الشيخان: means the hadith is mentioned in both sahih books with the same matn (content) but narrated by different sahabis or with differences in the narrator chain!
But some scholars seem to have their own definition of this, which differs from the general definition!
Mukhtalaf fih مختلف فيه and al hadith al mutawatir الحديث المتواتر
In istilah al muhaditheen (the terminology of the hadith scholars) there's no mukhtalaf fih مختلف فيه (can be translated as "in dispute about") AFAIK! But there's a subject area in istilah al muhaditeen called ilm mukhtalaf al hadith علم مختلف الحديث. The scope of this science is to find a midway or explanation to favorise between ahadith which seem to be contradictory. And there's also a topic in this subject area called mushkil al hadith مشكل الحديث which studies ahadith where the meaning is unclear and seem to contradict an other sahih hadith or a Verse from the quran, in this case the scholar is asked to check up possible meanings to give a final qualification (for more information see here in Arabic).
The conditions for sahih hadith have been derived from the conditions of al-Bukhari and Muslim etc. later and there's no specified number in the definition of tawator but some scholars said the minimum number is 10! But you may find ahadith in both sahih books which are ahaad which means they are not mutawatir at all!
And Allah knows best!
متفق عليه means that both Sheikh Bukhary and Sheikh Muslim agreed in both the content of the Hadith (namely the meaning) and share some of it's narrators.
Please refer to: https://www.islamweb.net/ar/fatwa/46516