I'm thinking at the time of St. Simon Stock the Carmelite habit looked something like what the Franciscan wore, until he was handed the scapular from Our Lady.
St. Simon was an Englishman that joined the Carmelite order soon after they arrived in England. In 1247 he was made the sixth General of the Order. He helped spread the Order throughout Europe and revised the Rule so that the Carmelites went from hermits to friars. His tenure wasn't easy, the Carmelites were picked on and persecuted by clergy and other orders, which makes me wonder, who were these mean orders? Mid 13th century Europe, hmm. The Cistercians? Benedictines? Dominicans? Franciscans? This calls for further study.
Anyways, it was so bad that the Carmelites had to get a Bull from Pope Innocent IV to stop the bullying. The Bull was nice, but the Carmelites also turned to their patron, Our Lady, and this is when the Holy Mother appeared to St. Simon and gave him the scapular and said,
"Hoc erit tibi et cunctis Carmelitis privilegium, in hoc habitu moriens salvabitur" (This shall be the privilege for you and for all the Carmelites, that anyone dying in this habit shall be saved)"
Thus begins the use of the scapular with the Carmelite habit and the origin of the ever popular devotion of the Brown Scapular, the small version of the Carmelite scapular.
Saint Simon Stock was never formally canonized, but has been venerated by the Carmelites since the 1500's when by decree his celebration was commanded for the Order. So if you are invested in the Brown Scapular, you are a de facto Carmelite and get to celebrate this feast, if not, you are Catholic and get to celebrate this feast.
Sanctus Simon Anglus, ora pro nobis.