Is Heads effectively the same thing as a detached LUKS header?

Assuming you keep the drive with the headers in a safe or on your person?

No. Heads works at a lower level (Bios/firmware).
Your device could already be compromised before it reaches the disk decryption state.

No, one difference is that heads can tell you if someone compromised your system, you don’t get that protection with detached header. If someone managed to compromise the detached header, you might not notice.

Detaching the header does protect the system if you need to leave it unattended, it’s effectively the same in that regard.