“Should we really call it praise and worship?”

Abraham and Isaac went up to the mountain top to worship. What was that worship? It was the sacrifice of Abraham's only son and the start of the promise in Abraham's heart. In my study of worship, it is all about the process of sacrifice. Giving of offerings of our money is a form of worship. We can worship during music if we are in a state of sacrificing things in our lives. But singing is praise. Singing in itself is not worship.

Look at "A History of Contemporary Praise & Worship: Understanding the Ideas That Reshaped the Protestant Church" by Lester Ruth and Lim Swee Hong for more on the terminology connected to the theology and where it came from, if you're interested.

Praise is a Subset of Worship

Wow, I’m really glad you pointed out how The Passion translation take praise into a password to God. Wow.