Great question. Thank you!
You are right, many times the words, “Baba,” “BapDada,” are interchanged. Matters could be a bit complex when “God” is referred as “Shiva,” “ShivBaba,” or “BapDada,” as well.
To my amazement, those words are not clearly understood by many BKs, let alone ‘researchers’ in religious topics.
For the sake of clarity and simplicity, the word “Baba” has been used widely to represent God, BapDada or even Brahma Baba.
When that simplicity is not enough, then we could add further depth.
In todays’ Murli (8-28-12) Brahma Baba was speaking saying that “he does not remember Baba all the time.” That means that in the “Sakar” -corporeal days, the difference was there.
There was a “Brahma Baba,” and a “Shiva,” God. When the connection was forged, then that was “BapDada.”
In the avyakt days ( Brahma Baba in his subtle role – angelic role) is known as “BapDada,” for that connection is stable. As a matter of fact, the first avyakt Murli in 1969 mentioned: “In the confluence age, God will be known as BapDada.”
BapDada is God for a BK soul. This is very important because our connection, our relationship with God is through the “middle man.” (Brahma)
That connection manifests through us Brahmin souls, through the sanskaras of Brahma Baba.
In short, Brahma Baba gives “personality” to God, the point of light, Shiva.