How have I to understand in what those quantum numbers refer for ortho and para water?
It's explained in the first link you gave in the previous paragraph:

"The rotational quantum states of the asymmetric rotor, i. e.,
water, can be classified by $J_{K_{a}K_{c}}M$, with the total angular
momentum quantum number $J$, the projection labels $K_{a}$
and $K_{c}$ onto the molecule-fixed a and c axes as defined in
Figure 1 respectively, and the projection quantum number
$M$ onto the space-fixed $Z$ axis."

Do you know how angular momentum in quantum mechanics works? You can look at the projection of the angular momentum onto a specific axis and the total angular momentum. Turns out the Heisenberg Uncertainty Principle prevents you from knowing the angular momentum projections along more than one axis at once...