In the phrase that follows we say, كما صليت على إبراهيم وعلى آل إبراهيم translated as, “just as You sent prayers upon Ibrahim and upon the family of Ibrahim.” And with this, we are effectively invoking a preceding action of Allah’s, for a subsequent one to occur. So we are saying, “Just as You, Glorified be You, previously bestowed favour upon Ibrahim - peace be upon him - and his followers, so extend Your favour to Muhammad - peace be upon him - and his followers.”
And the supplication that follows is a repeat of this, when we say, اللهم بارك على محمد وعلى آل محمد كما باركت على إبراهيم وعلى آل إبراهيم, commonly translated as, “O Allah, send blessings upon Muhammad and on the family of Muhammad, just as You sent blessings upon Ibrahim and upon the family of Ibrahim.” But in this case, we are asking Allah to bestow His blessings and not His prayers. The root meaning of the word for blessing بركة signifies continuation and endurance, and blessings are so-called because they imply an abundance of good, its continuity and its enduring presence in action.
So when we make these supplications to Allaah in the second part of the tashahhud, we are esesntially saying, “O Allah, just as you have sent Your most complete, encompassing prayers and continuously bestowed enduring goodness upon Ibrahim - peace be upon him - and his family and followers, then I ask of you to do the same upon Muhammad - peace be upon him - and count me among those followers.”