The grammatical parsing of “Allahumma” is as follows: “Allah” is a vocative noun, indeclinable with the ḍammah ending, and in the accusative position. The meaning of “Allah” is: the One who possesses divinity, whom everyone who worships worships.
His statement, “Send blessings upon Muhammad”: It has been said that blessings from Allah mean mercy; from the angels, seeking forgiveness; and from human beings, supplication.
Thus, when it is said, “The angels sent blessings upon him,” this means: they sought forgiveness for him.
When it is said, “The preacher sent blessings upon him,” this means: he supplicated that blessings be bestowed upon him.
And when it is said, “Allah sent blessings upon him,” this means: He showed him mercy.
This is well known among the scholars, but the correct view is otherwise: sending blessings is more specific than mercy. This is why the Muslims have unanimously agreed that it is permissible to supplicate for mercy for every believer, while differing over whether blessings may be invoked upon anyone besides the prophets. Had sending blessings meant mercy, there would have been no difference between them: just as we supplicate for mercy for a particular person, we would invoke blessings upon him.
Moreover, Allah, Exalted is He, says: “Upon them are blessings and mercy from their Lord.” [al-Baqarah 2:157] He conjoined “mercy” to “blessings,” and conjunction entails distinction. Thus, the indication of this noble verse, together with the scholars’ usage of “blessings” in one context and “mercy” in another, makes clear that sending blessings is not the same as mercy.
The best explanation given of it is what Abu al-ʿĀliyah said: Allah’s sending blessings upon His Prophet is His praise of him in the highest assembly. (1)