The C in CR2032 means lithium fwiw. As in it's lithium either way.

The LiR2032 (rechargable lithium) are slightly higher voltages but pretty much the same total energy.

Fwiw if you ever have electronics that require 3V minimums the LiR2023 is better than the CR2032 since it's 3.7V vs 3V in the same form factor. It's common knowledge that the ESP32 for example can glitch on a CR2023 since it needs 3V minimum but it'll actually run fine on a LiR2032.