Aunt Viv flys Tray out to visit Will because he's homesick, just like she does with Ice Tray in the original series. However, Ice Tray sparks up a romance with Hilary during his visit — something the reboot doesn't rehash.
Will discusses his emotional distance from Tray with Aunt Viv. In "Bel-Air," Will is upset that Tray thinks he's changed from who he was back in Philly, and Aunt Viv validates that trauma is bound to affect people in different ways. In "The Fresh Prince," Aunt Viv doesn't like Ice Tray because of his budding romance with Hilary, and she voices how Will is essentially more polished than him. In both, however, Will defends their friendship, noting all the hardships they've been through since childhood.
Will calls Carlton "C," a term of endearment he uses in the original series. In "The Fresh Prince," Will also calls Carlton "C Note" in reference to his love of Broadway.
Will decides to stay in Bel-Air despite his mom's wishes, noting his new opportunities, friendships, and finishing out the school year. In the original series, his mom asks him to move back to Philly after graduating high school, but he decides to stay for college.