At the base level, no difference at all. However you might get lucky that a certain property takes kindly to your GHA being of that chain's, maybe gives you an unexpected room upgrade or something but don't hold your breath for it. If you have plans to stay at a particular chain and accrue status, then sign up for that chain's loyalty program. Link below from Kempinski for illustration..
https://www.kempinski.com/en/hotels/loyalty-programme/