鍋: A cooking pot and a hotpot meal
Compare a large 鍋 used to cook vegetables with 鍋 as a hotpot meal someone wants to share with family. Use the surrounding verb and context while preserving the wish.
鍋 as a cooking vessel
「大きな鍋で野菜を煮込んだ。」 — “I simmered vegetables thoroughly in a large pot.” 大きな鍋で names the large pot used to cook the vegetables. The size modifier and the tool role of で identify the vessel rather than naming the vegetable dish.
野菜を煮込んだ reports the cooking action. The pot is its tool and the vegetables its object, so keep those roles distinct.
鍋 as a meal to share
「寒い夜は家族で鍋を囲みたい。」 — “On cold nights, I want to sit with my family around a hot pot.” 鍋 here names the hotpot meal the person wants to share. 囲みたい expresses a wish to gather around it with family, not a completed meal in the past.
Read the cold-night setting and 家族で as the participants. The same noun has a different focus when describing a shared meal rather than the vessel used for cooking.
Use the surrounding expression
大きな鍋で煮込む presents the pot as a cooking tool; 家族で鍋を囲みたい focuses on a hotpot meal. The particle alone is not an absolute meaning rule: follow the verb, modifier, and participants.
The first example reports past cooking, while the second expresses a wish. Keep that modal difference when distinguishing the senses, without adding that the family already ate the hotpot.
Does 鍋 have the same meaning in 「大きな鍋で野菜を煮込んだ」 and 「家族で鍋を囲みたい」?
Show the answer and why
The first is the large cooking pot; the second is the hotpot meal the person wants to share with family. Context distinguishes the vessel and the meal, while 囲みたい remains a wish.