Do I need a Milk Pail for every cow stardew?

Excuse me, but I'm a bit confused about the specifics of dairy farming in Stardew Valley. I understand that cows are a valuable source of milk, but do I really need a separate milk pail for each cow? Is there a reason why one wouldn't just use a single pail to collect milk from multiple cows? I'm trying to optimize my farming efficiency and want to make sure I'm not wasting resources. Can you clarify the best practice for milk collection in Stardew Valley?