First of all, as most readers are probably aware, customs vary regarding exactly how long to wait between meat and dairy, and there are indeed customs that differentiate between actual meat and poultry in this regard. However, I believe that the more accepted custom is to wait the same amount of time after meat or poultry.
Like in all matters of halakha, there are differing opinions as to equating meat and poultry in this matter. The Rashba, Ritva, and Piskei Rid (2nd version, all to Chullin 105b) believe one would not have to wait an extended period of time after fowl. Their reasoning is not because poultry 'was once not considered fleishigs' (because after all, the decree to consider it 'fleishigs' may have come before the custom to wait afterwords), but because we hold that poultry is not Biblically ordained as meat. While Tosfos (to 104b) acknowledge that the common practice is to wait the same amount of time, they say that this must be because we believe that poultry is Biblically considered meat, which we actually do not. The Ohr Zarua (1:460) believes that this is the opinion of Rashi as well.
However, the Rambam (Hil. Maachalos Asuros 9:28) writes that there's no difference between the meat of an animal or fowl in this case, and the Riaz (Piskei Riaz Chullin 1:17) writes that such has always been the custom. The Meiri, in his book discussing the justifications of various Provincial customs (Magen Avos inyan 9), discusses at length the custom to wait for the same amount of time between poultry and dairy. He writes that when it comes to Rabbinic decrees, כל דתקון רבנן כעין דאורייתא תקון, these decrees should be treated in the same way as the original Biblical command that the decree is coming to safeguard (note: this isn't exactly the standard interpretation), and because it appears from the Gemara (Chullin 104b) that poultry is equally prohibited to be eaten at the same meal as meat (which is part of the reason for waiting six hours, the usual time between meals). The Rosh (siman 5) also writes that this is the custom, and this is how it's recorded in the Shulchan Aruch (Y.D. 89:1) and agreed upon by the Shach and Gra there.