The holy spirit is vague in the same way God the father and God the son are vague. We know a few of their attributes, like the fact that the Father created the world or the Son incarnate in Jesus Christ, but that is about it. As for the Holy Spirit, it is the part of God that is ever present on earth and who is supposed to help humanity, give them strength and counsel them. While often forgotten, his sincere ministry is to point away from himself to the wonder of God the Son and God the Father, that doesn't mean various religions have not defined him.
For example, in Islam the Holy spirit is the Archangel Gabriel, who is the messanger to all prophets (they don't beleive in the trinity.)
I have found no religion where Mother Mary and the Holy Spirit are one and the same, and it certainly isn't true in christianity. He is very different from Mother Mary, since he is the one who conceived Jesus Christ with her.