Interesting: On 87b, the Gemara says, after saying that we went out of Mitzraim on 15 Nisan, since that was Thursday, that means that Rosh Chodesh Iyar was on Shabbos. It then proceeds to Rosh Chodesh Sivan, etc.
On 88a, however, the Gemara works backwards: since the day we went out (15 Nisan) was Friday, that means that Rosh Chodesh Nisan was also on Friday** and then the Gemara goes R"Ch Nisan-->R"Ch Iyar-->R"Ch Sivan.
Why the backward step to R"Ch Nisan?
Gershon
Interesting it is, but I don't think its of any major significance. Given what day the fifteenth of Nisan took place, there are two ways of working out on which day Rosh Chodesh Iyar must have fallen ... one by counting the fifteen days to the end of the month, the other, by noting that Rosh Chodesh occurred on the same day, and applying the principle that Rosh Chodesh Iyar will take place two days later.
It is clear from the Sugya that these two Beraisos were learned by two different authors, so it is not even a Dochek to say that one Tana used the one method, whilst the other Tana used the other method.
be'Virchas Kol Tuv.
Eliezer Chrysler.