Intensity is defined as power / area, where power = energy / time. Now with some dimensional analysis and playing around with units, we can see the following:
Intensity = power / area = W / m^2 -->
Intensity = (J / s) / m^2 = J / (m^2 * s) -->
Intensity = (J / (m^2 * s)) * (m / m) (you can multiply with m / m because it's the same as multiplying by 1) -->
Intensity = (J / m^3) * (m / s)
Now m / s is the units for velocity. J / m^3 is energy per unit volume or energy density (so intensity = energy density * wave speed). Energy density is a property of a wave and depends on specific wave characteristics. Sound waves are mechanical waves and they require a medium for travel. Sound energy density depends on medium (such as atmospheric) properties since you are dealing with pressure waves. Electromagnetic waves do not require a medium and can freely travel in a vacuum. Electromagnetic energy density consists of electrical energy density (from electric fields) and magnetic energy density (from magnetic fields). These are intrinsic to the wave itself.
Because electromagnetic waves can be quantized into photons, the energy density = (energy density / photon) * number of photons, and so intensity is directly related to the number of photons.
Energy density is often synonymous to pressure by looking at units. J = N * m , so J / m^3 = (N * m) / m^3 = N / m^2 = Pa. So sound energy density is related to sound pressure by the following relationship:
Sound energy density = sound pressure * (particle velocity) / (wave speed), so:
Intensity = sound energy density * wave speed -->
Intensity = sound pressure * (particle velocity)/(wave speed) * wave speed -->
Intensity = sound pressure * particle velocity
Electromagnetic radiation pressure is generally the same as electromagnetic energy density because the photons travel in the same speed as the wave.
So to summarize, intensity is related to energy density of waves dependent on specific wave characteristics. Sound waves are mechanical waves and depend on medium properties. Electromagnetic waves can travel in a vacuum and only depend on the electric/magnetic field properties intrinsic to the waves (and also the number of photons when you quantize the waves).
