I would like to know if there is a difference between an adsorption isotherm which is determined by varing the concentration of the adsorbate with a fixed masse of adsorbant, and the opposite.
Theoretically, no. However you need to bear in mind dynamics. It is most straightforward usually to use your first scheme, starting at low concentration and adding adsorbate to it in stages. Adding more adsorbant to a system already at equilibrium requires adsorbate to desorb first then readsorb, which might be a slow process and likely to lead to errors.
Stuart
I agree with Stuart. Since there are often separate adsorption and desorption isotherms, it could be that you will end up with both processes happening concurrently and get a point in between.
Just for interest, I thought I'd try to put an illustration in here.