What is the interpretation of "Subhanaka wa bihamdika" and what is the difference between it and "Subhan Allah"?

"Subhanaka wa bihamdika" consists of two words: "Subhanaka" means glorifying Allah and declaring Him free from all imperfections, and "wa bihamdika" means praising Him for the perfection of His essence and attributes. There is no difference between "Subhanaka" and "Subhan Allah" in terms of meaning, but "Subhanaka wa bihamdika" is more comprehensive and inclusive due to the addition of praise (hamd) and commendation.