Potion fight is a combat situation where player success is tied to number of potions(consumable resources in general that he own).
Its usually due game design favoring consumables over innate heal/regen skills.
In PvE situations, players might drop hundreds of potions before or during the battle to pick up later, to avoid losing entire inventory of them at once.
In PvP characters with larger inventories have an advantage which allows to "out-drink" players of comparable DPS.

In general potion fights are a symptom of bad design and attempts to hide potion use through clever consumable mechanics will not work.
The proper solution is to have either no potions at all or have a high cooldown period that prevents their use in battle, with skills that add healing/regen available to all classes(to avoid PvP imbalance).

The idea of consumable-centric RPG is conceptualizing skills into gold-sink items: Scroll of Healing, Staff with 100 healing charges, Potion that adds Fire resistance,etc vs Skill-centric RPG which focuses on skill use and items granting bonus to skills: Staff with +1 to Healing Skill.