Both are "24C02" which is a generalization. Second one not being specific about what it actually is, there are a ton of different 24C02. Generally all 24C02 are mostly compatible but there may be differences which can be an issue in some cases. The issues may be with operating voltage range, presence of adress pins (if not all of them are connected to GND), maximum clock frequency if a high clock speed is used in particular device. Also they may have different maximum page write size. Generally all of that is not an issue, however device may be deing something out of particular IC spec.
As of max I2C speed, it's very unlikely this meter uses over 400kHz.