HP Stroll is an auto-ability that can be found on dropped armor, or customized to an armor with Stamina Tablet items. The character with the respective equipped armor in the current active battle party will gradually recover HP as the party moves about the field.
Move-HP Up is a proactive ability that costs 13 CP to equip. It is active for the entire length of Field Music Sequence (FMS). The character regains some HP for every GOOD or better and medium strength. It is learned by Onion Knight (level 80), Bartz (level 70), Zidane (level 70), Orlandeau (initially), Rikku (level 85), Ciaran (level 65), and Cosmos (level 85). It can be taught to any character by using the Move-HP Up Scroll.
HP Stroll is learned innately by Paul, Montana, Kaede, Guy, Gilbert, Riley, Bartz, Dark Knight Cecil and Snow. It can also be equipped via HP Stroll materia, the Cat's Bell accessory, and Titan's skill grid. Nine learns Double Recover which combines HP and MP Stroll.