The Italian Mushroom Consortium recognizes six varieties of commercialized mushrooms: prataiolo bianco (white field mushroom, usually called by its French name, «champignon,» in Italy), prataiolo crema, portobello, pioppino, pleurotus (or gelone), and cornucopia.

http://www.corriereortofrutticolo.it/2016/07/18/nasce-fungo-italiano-certificato-origine-sostenibilita-alla-base-del-progetto/

I love this question. Both portobella and cremini are the common brown mushroom which has been cultivated in this country for more than a century. As previously noted the names are just marketing. They sell better if you give them a fancy Italian name.

Portobello (or portabella) mushrooms started as a genius way to market overgrown cremini mushrooms. The mushrooms called cremini came from Italy, the overgrown version we know as portobello came from American marketing. All delicious!!