Besides PIN and PUK, there are a few additional terms for the eSIM:
eSIM Profile: it contains all the info that is also stored on the eSIM.
Activation code: You need this to activate and download your eSIM profile. You can get it either as a QR code or a very long code in digits (ask provider if you did not receive it) for manual activation.
PIN: Some manufacturers also call the PIN a confirmation code. You need the 4-6-digit PIN to confirm the activation of the eSIM profile. You will receive the PIN together with the activation code.
EID: The EID is the serial number of your device indicating that it supports eSIMs. It is printed on the packaging, for example. You can also find it under Settings in the device info.