Objection 1. It would seem that in the angel to understand is to exist. For in living things to live is to be, as the Philosopher says (De Anima ii, text. 37). But to "understand is in a sense to live" (De Anima ii, text. 37). Therefore in the angel to understand is to exist.
Objection 2. Further, cause bears the same relation to cause, as effect to effect. But the form whereby the angel exists is the same as the form by which he understands at least himself. Therefore in the angel to understand is to exist.
On the contrary, The angel's act of understanding is his movement, as is clear from Dionysius (Div. Nom. iv). But to exist is not movement. Therefore in the angel to be is not to understand.
I answer that, The action of the angel, as also the action of any creature, is not his existence. For as it is said (Metaph. ix, text. 16), there is a twofold class of action; one which passes out to something beyond, and causes passion in it, as burning and cutting; and another which does not pass outwards, but which remains within the agent, as to feel, to understand, to will; by such actions nothing outside is changed, but the whole action takes place within the agent. It is quite clear regarding the first kind of action that it cannot be the agent's very existence: because the agent's existence is signified as within him, while such an action denotes something as issuing from the agent into the thing done. But the second action of its own nature has infinity, either simple or relative. As an example of simple infinity, we have the act "to understand," of which the object is "the true"; and the act "to will," of which the object is "the good"; each of which is convertible with being; and so, to understand and to will, of themselves, bear relation to all things, and each receives its species from its object. But the act of sensation is relatively infinite, for it bears relation to all sensible things; as sight does to all things visible. Now the being of every creature is restricted to one in genus and species; God's being alone is simply infinite, comprehending all things in itself, as Dionysius says (Div. Nom. v). Hence the Divine nature alone is its own act of understanding and its own act of will.
Reply to Objection 1. Life is sometimes taken for the existence of the living subject: sometimes also for a vital operation, that is, for one whereby something is shown to be living. In this way the Philosopher says that to understand is, in a sense, to live: for there he distinguishes the various grades of living things according to the various functions of life.
Reply to Objection 2. The essence of an angel is the reason of his entire existence, but not the reason of his whole act of understanding, since he cannot understand everything by his essence. Consequently in its own specific nature as such an essence, it is compared to the existence of the angel, whereas to his act of understanding it is compared as included in the idea of a more universal object, namely, truth and being. Thus it is evident, that, although the form is the same, yet it is not the principle of existence and of understanding according to the same formality. On this account it does not follow that in the angel "to be" is the same as 'to understand.'
Source: Summa Theologica (New Advent)