Most likely the pore size distribution will not be the same. Remember that the BJH not suit for micropores.

Adsorption and desorption branches in mesoporous materials show hysteresis because the filling and emptying of the pores occurs in different ways.

The BJH method is derived based on the Kelvin equation which considers the formation of a meniscus, which occurs during desorption.

Adsorption, on the other hand, occurs by formation of layers instead of meniscus.

Then, if you use BJH equation with the adsorption branch you will get the wrong results because there is no formation of meniscus.

If you want to use the adsorption branch, you need more advanced methods such as NLDFT or QSDFT.

Also see a related thread here:

https://www.researchgate.net/post/Why_does_mesoporous_material_have_hysteresis_loop_in_adsorption-desorption_N2_curve

(In the future, I might add a movie I made showing the differences between the two processes for a simple pore.)

Hystersis loop observes when the pores shape is such as open channels so that capillary condensation occurs in these channels. Probably, as Mr. V.-Burgos mentioned, you synthesized a mesoporous structure with different size of channels. In addition, when we want to measure pore volume, we must desorb the gas molecules which deposit on the pores of the sample.

Ce phénomène observé, est tout simple, vous avez deux processus l'adsorption et la désorption, comme une sorte d'aller-retour, la probabilité pour que l'aller soit pareille au retour est faible, du coup on aura des valeurs différentes. L’hystérésis matérialise ce phénomène.

De plus l'adsorption est souvent facile, mais la désorption difficile, en plus on ne désorbe pas totalement ce qui a été adsorbé.

If you use the desorption curve for the Pore Size Distribution then you are assumming cylindrcal non-intersecting pores with a hemispherical meniscus. If you use the adsorption branch then the two extremes are a cylindrical meniscus with pores open at both ends or a hemispherical meniscus if they are closed at one end. Using these two extremes can lead to pore widths that are greater or smaller than hose obtained with the desorption curve. With the Micromeretics software you can mix the two extremes in any proportion that you like in order to get the data from the adsorption curve to coincide with that of the desorption curve. However, personally I consider this just juggling with the mathematics and so prefer the desorption branch since the user can not "fix" the result.