It would seem to be a natural pairing of concepts – the giving and the receiving being the two sides of the same action and apparently interchangeable as descriptions of the event.
Nevertheless, they are not identical.
Each has its own particular meaning.
As the Kabbalah puts it, the giving of the Torah is a movement from above to that which is below, while the receiving is a movement from below reaching upward.
And in the dimension of time, the giving of the Torah is essentially a single act, while the receiving of the Torah is a diversified and continuing process in history.”
From an essay, “Torah Eternal,” by Rabbi Adin Steinsaltz