[The Difference Between “One Who Wills By His Essence” and “For” His Essence”]

Answer – and Allah is the One who grants success: The doctrine of the Ashʿarīs, as in the book al-Qalāʾid, is that Allah, exalted is He, is One Who wills (murīd) by a pre-eternal will (irādah qadīmah). End.
As for the Najjāriyyah, they say that Allah, exalted is He, is One Who wills, but that He, exalted is He, does not have an attribute called “will” as the Ashʿarīs say. Rather, in their view, He wills by His Essence (bi-dhātihī), just as we, the Zaydiyyah, say: He, exalted is He, is Knowing by His Essence (ʿālim bi-dhātihī), Powerful by His Essence (qādir bi-dhātihī), and Living by His Essence (ḥayy bi-dhātihī).
This is one of two possibilities. The second possibility is that they – i.e., the Najjāriyyah – intended by the bāʾ (in bi-dhātihī) the meaning of causality (as “because of”), and on that basis their doctrine would agree with the doctrine of the Ashʿarīs; because what appears is that the Ashʿarīs intend by the lām (in li-dhātihī) the meaning of causation (taʿlīl). So, on this reading, there is no difference.
However, on the first possibility, the bāʾ is for the instrument, as in “I wrote with the pen (bi-l-qalam),” and on this reading the difference is evident.

Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.3