Just because they speak a related language (Turkic) does not mean that they are the same people.
Actually, Turcomen are ethnic Turks who speak Arabic. Uzbeks and Anatolian Turks are distantly related. Turcomen and The Tukish/Ottoman/Seljuk Turks are decended from the same group, the Ghuzz-Seljuk and general Turkmeni migrations following 1040.
The Azeris of Iran and Azerbaijan are part of the same group.
As for the general article, are we to take the statement of a few groups in either Iraqi controled territory or Kurdish controlled territory at face value?
Well, under whose face value do you want to take it under then? Certainly the Turks of Turkey do not seem to speak for the these "Turks".