On the consistancy of potions and their containers in a medieval setting:
First off, potions are not -allways- a liquid. The very definition you gave states that they are -usually- liquid. That is the same as saying the sky is -usualy- blue. Is it always? No. A potion can be a mixture of something dry, or even a paste, set in folded paper. A potion can also be any size you can imagine.
Now for the containers. Let's look at this logicaly. Potions designed for instant healling in battle settings would have to be two things. One, they would have to be easy and fast to consume, in or out of battle. This leads to the arguement that they would be small. Now, to make them fast to drink (since they do seem to be liquid in this game), despite the small opening, they would have to be soft, and likely made out of a cured animal hide (is that what rat hides are used for?) or internal organ. Further supporting this is the fact that glass and clay are heavy, hard to drink out of, and very easy to break. By the time you were done being pummelled by a foe, half your potions would be crushed. Then, take into acount that glass was very expensive to make in medieval times, and would not be handed out like candy.
Taking all the facts into consideration, you are left with the assumption that potions are a very potant liquid contained in a durable, cheap, small, and soft container that degrades when dropped. A cured bladder from a small animal would easily fit all of those criteria. Glass, clay, and even metal would not.