"SSD" means "solid-state disk," meaning it uses flash memory instead of spinning mechanical disks.
"NVMe" is a logical interface, meaning it is a communication standard. (Personally, I'd call it a protocol.) That means it is not a physical standard, but rather, it dictates the terms of data being communicated.
"AHCI" is also a logical interface. It is what NVMe replaces. NVMe can be implemented on PCIe, while AHCI can be implemented on both PCIe and SATA.
SATA and PCIe are both bus interfaces. So that means they dictate physical connections and electrical standards. Again, the SATA bus will be paired with the AHCI logical interface, while the PCIe bus can be paired with either the AHCI or NVMe logical interfaces.
So any SSD can come in 3 types:
(1) SATA with AHCI
(2) PCIe with AHCI
(3) PCIe with NVMe
#2 was short-lived. A few PCIe drives were released before NVMe was released. Hence PCIe with AHCI. But now virtually all SSDs are either #1 or #3.