Commentary for Avodah Zarah 149:4

And they do not disagree. Rav and Shmuel [do not disagree], according to the language of Pumbedita, except that Rav does not count the final [rinsing with] water, and Shmuel does count the final [rinsing with] water. And there are those who explain that "they do not disagree" refers to Sura and Pumbedita, except that Sura does not count the final [rinsing with] water and that Pumbedita does count [the final rinsing]; but, Rav and Shmuel disagree. And this is the meaning of the words "two, three": Two [steps are necessary] for a dry [vat]: water and ash; three for a moist [vat]: ash and water and ash. And Shmuel says three for a moist [vat] as stated, but for a dry [vat], four: water and ash, water and ash; in all cases, [Shmuel] requires ash twice. And in Pumbedita it was taught that Rav [required] three and four [steps]: For a dry [vat], three: water and ash [and] water. And we also have this in Sura, except these [i.e. the Pumbedita prescriptions] count final water [for rinsing]. And for a moist [vat], four [steps are required]: ash and water, ash and water; and according to Shmuel, for a moist [vat], four [steps are required] as stated, but for a dry [vat] five [steps are required]: water and ash, and water and ash, and water, such that a dry [vat] also requires ash twice. "And they do not disagree refers to Sura and Pumbedita, etc." But, Rav and Shmuel disagree regarding a dry [vat] both in Sura and in Pumbedita in that Rav only requires ash once and Shmuel requires [ash] twice. This is reading of my father, my teacher, may he rest in peace, and this seems to me [to be the correct reading]. The first reading [is that of] my teacher, and it is difficult for me since in the language of Sura, Rav and Shmuel certainly disagree. What is the difference [of opinion]? Rav counts final [rinsing] water and Shmuel does not count final [rinsing] water. For Shmuel, [the] four and five [counting] requires that we teach [that Shmuel is counting the final rinsing water]. This is reasonable according to Pumbedita even though Rav does not count [the final rinsing water] and Shmuel does count [it]. This is convenient because the disagreement between Rav and Shmuel is not substantive, [it is] only [a disparity] in the counting of the final [rinsing] water. But, according to the language of Sura, there is still a disagreement [between Rav and Shmuel], which is difficult for me.