1) Large Pot = Pot, for some reason in the craftdwarf's is called "large pot" and the kiln calls it "pot", in the end both produce "large pots"
2) Plant stacks supposedly can go until 11 if I recall correctly, nevertheless a Barrel and a Pot are basically the same with the exception on the capacity they can store
3) Containers have a capacity value, that value translates into liquid capacity and solid capacity is 1/10th of that, in the case of barrels is 100 Liquid and 10 Solid, that's why you can store up to 10 prepared meals/plants/etc... and up to 100 liquid, with booze is hard to tell because no stack would be so big to produce 100 units of booze, but Milk is emptied from the buckets to the barrel up to it's capacity, so in theory you can have a barrel with 100 individual stacks of milk (from the same animal species)
4) Pots have a capacity of 60.000 in the raws, that means 60.000L and 6.000S items, the trick is convincing your dwarves to store more than 100L and 10S in the pots....
5) some people report that the pots aren't even used, some report that they are used with the same capacity as barrels, and some report them being used to stored huge amounts, I have a pot with 500+ prepared meals....
6) How to do it?:
* Pots seem to have lower priority than barrels, once you don't have available barrels (either by use, forbidding, locking doors, etc) dwarves start using pots.
* Alternatively you can dump a pot in the stockpile by setting an overlapping garbage zone...
* The stockpile max barrels setting seem to control not only how many barrels can be used but how many capacity units can be stored inside the containers in the stockpile, for every barrel you add 100 units...
* I theorize that if you have a 60 tiles stockpile, with one large pot, with max barrels set to 60, and you manage to avoid any other container to get to the stockpile (or forbid the ones that get there) you could get a pot able to store 6.000 solid items or 60.000 liquid items (probably only possible with milk).
* For example if you have a meals stockpile with one pot and 2 max barrels that pot will be able to store up to 200 meals (as long as you keep out or forbid the second barrel/pot) if you rise the max barrels to 6 you can store 600 and so on...
* Every Barrel/Pot added to the stockpile claims 100 capacity units that can't be used by other containers, the trick is to set up the max barrels to he desired capacity and keep out other containers to claim that capacity so it's used by the large pot....