Does "Alhamdulillah" mean glorification and magnification, and does it include praise, and is there a difference between them?

"Praise (Al-Hamd) entails glorification (Al-Ta'dheem), which is the declaration of the praiseworthy's virtues coupled with love, veneration, and glorification for Him. The difference between Al-Hamd, Al-Tamjeed (magnification), and Al-Thana' (commendation) is that Al-Hamd is commendation for beautiful actions, Al-Tamjeed is commendation for attributes of majesty, while Al-Thana' encompasses both."