I asked this question on Mi Yodeya and this answer says that these were different measuring utensils (standard weights). This answer is based on the Targum, an early translation into Aramaic; I don't have the linguistic skills to evaluate that myself, but it's generally held to be a faithful translation + clarifications (like this).
When transactions were paid for by weight of (e.g.) silver instead of by government-issued money, a merchant would use a balance-style scale to weigh the tender on one side against fixed weights on the other. Rashi, Tosofot, and the Targum (as cited in the linked answer) are talking about these kinds of fixed weights.
Please note: This answer was written for a neutral, academic audience
and is not intended to be interpreted in the context of a religious
belief or doctrine.