If you click on the coffee menu in this link: https://www.devans.in/index.php?route=common/home you will see strong, very strong, mild etc. options.
What do these options refer to in Coffee? Amount of caffeine? Amount of bitterness?
It usually refers to how long the coffe was roasted as roasting give certain taste in beans.
So it's taste indicator. Mild is very light, sometimes called washed-down (as some places try to pass medium strength as mild by diluting it with water). It should have almost no dry aftertaste (I think you mean that by bitterness). It would also be not so acidic.
Strong coffe is the one that people usually ad milk or sugar as it most dry, acidic, and toasted taste. Brew itself will also have oily/rainbow film on surface.
Light coffes (so mild or any that was toasted shorter than 10 minutes) have the largest amount of caffeine. But that also depend on beans type (Arabica, robusto and so on)
Specific to this website, where they enlist their "Arabica peaberry" dark roast and french roast as very strong, and their espresso and Viennese blend as Strong; I can conclude that they use roast degree as a metric for strength.
I can easily say that it is not based on caffeine, as the most stronger one is an Arabica peaberry. If it was based on caffeine amount, it should be a Robusta instead of an Arabica. We know that being a peaberry bean or not does not really influence the caffeine amount.
Viennese blend is probably a Viennese roast. Also, an espresso blend is a quite dark roast to decrease the acidity of the overall blend. The reason is, the espresso preparation technique is known to add additional acidity to the final cup of coffee. So, roasters prepare a bit more darker roasts to decrease the acidity for coffee that will be used for espresso.
To me, people are referring to flavor preference when using terms like mild, strong, and very strong to describe coffee taste. It can also be used to describe color or caffeine content. Someone may like the flavor of a dark roast but call a coffee strong due to high caffeine content after drinking too much.
I always heard the dark roasts have less caffeine, but not necessarily, according to kicking roast ~ https://www.kickinghorsecoffee.com/en/blog/caffeine-myths-dark-vs-light
"During the roasting process, a bean loses its mass. The density of the bean changes; beans that are roasted longer are less dense. That’s why you have more beans by mass of dark roasts. "