They are not same, it does not matter if TTP gives pledge to IEA or not, Zabiullah Mujahid IEA spokesperson has clearly said that TTP is a different group with their own aims and agendas that have nothing to do with IEA.A brief on your pointers
1) Yup, they backtracked on the Doha Agreement which covers Pak as well
2) TTP gave baith (pledge of alliance) to IEA leader, if they had nothing to do with TTP they could have ejected it
they are the same TTP and Taliban
Few Months ago TTP blamed Pakistan and IEA of collaborating(double game) and asked US for help.