Usage:
A Hot Cup is used for hot drinks such as coffee, tea, and hot chocolate.
A Cold Cup is used for cold and frozen drinks such as soda, lemonade, boba, slushy, and ice cream.
Material:
Hot Cups are usually made from paper material.
Cold Cups are usually made from plastic material.
Sleeves:
Hot Cups need sleeves to protect users from getting burned from the steaming heat.
Cold Cups are recommend to have sleeves to absorb the cold condensation and keep users hands from getting wet.
Cup Sleeves Blog 