What is the difference between ideal stages and transfer units in a packed bed gas absorber? I am having a hard time grasping what these two concepts are supposed to mean and how they differ. What I know so far is:

In a counter-current gas absorber, if we set the inlet and outlet concentrations of solute in gas and liquid, and also have control on the ratio of gas to liquid flow rates, we can find the outlet concentrations by making a "step" like a staircase (with the number of steps equaling the number of stages) from the operating line to the equilibrium curve.



I understand where this comes from. When we draw a "step", we are equating the two outlet concentrations to be in equilibrium.

Now, for the number of transfer units, we usually find this out by using the integral formula:

$$\text{NTU} = \int_{y_1}^{y_2}{\frac{dy}{y-y*}}$$

where $y$ is the operating line solute concentration in gas phase for a given $x$, i.e. solute concentration in liquid phase, and $y*$ is the equilibrium curve solute concentration for the same $x$.

What I have noticed is that often, the NTU is not an integer, it can also be a fraction. And this fraction, multiplied by the height of transfer unit (HTU), gives the total height of the bed needed for such a transition.

I am confused. I dont understand what NTU is exactly, or better, what a transfer unit is. I would greatly appreciate some guidance.
A transfer unit gives the change of composition of one of the phases equal to the average driving force producing the change
Source: http://www.separationprocesses.com/Absorption/GA_Chp04c.htm

So to phrase it differently, for some ideal zone in the absorber that has a particular value to the average mass transfer driving force, there will be a fixed change in the phases present at that ideal zone.
NTU is somewhat analogous to the total number of theoretical stages if the operating and equilibrium line are straight and parallel.
There is no direct physical interpretation of what a transfer unit. If you design any appreciable size packed bed tower, you will find that the vendors of the packing will use a lot of empirical correlations for their own products to determine separation efficiencies and other related parameters.