Is there a physical difference between the intensity and intensity level of the wave?

Yes, there is a difference between the intensity and intensity level of the wave. The intensity of sound waves is the amount of sound energy passing through a surface per unit surface area per unit time when the surface is perpendicular to the propagation of the wave, while the intensity level is the relative value of the intensity with the reference to the threshold of hearing. These two terms are related by the formula, \(L=\log_{10}\left(\frac I{I_0}\right)\), where I is the intensity of sound wave and I₀ is the threshold of hearing, L is the intensity level. I is measured in Wm^-2 while L is in bel.

The absolute intensity cannot be measured and avoided internationally and the relative value of intensity is measured which is called intensity level.