Hardware – What are the differences between HSM and SE?

What are the differences between a Hardware security module (HSM) and a Secure element (SE)? Can both terms be used interchangeably?

I came across various related issues (TMP vs HSM and TPM vs. SE), but the different definitions of HSM and SE found online were very closely related.

To which category belongs a cryptographic coprocessor with a secure hardware key storage, such as the Microchip ATECC608A?