The connotation of existence and the notion of actus essendi are closely related, but they are not equivalent concepts. In the present context it should suffice to say that existence applies to that which exists in any way whasoever, whereas actus essendi applies only to that which exists as a subsisting extramental thing.
The notion of existence reflects the facticity of any state of affairs. Of anything that in any way whatsoever exists, one can say that its existence is a fact.
Actus essendi, on the other hand, refers to an innermost principle which serves as the ultimate ground of all the actuality, perfection, and knowability instantiated in a subsisting extramental thing of nature.
The possession of actus essendi necessarily results in having existence, but among existing things there are many which are not subsisting extramental things.
With reference to God, for example, Aquinas explains that knowledge of the existence of God is not the same as the knowledge of His act of being, that while we cannot know God’s act of being nor His essence, we are able to know the existence of God.