NVMe is the new logical device interface spec; it's the new way to speak to PCIe based SSDs. The old interface spec is AHCI which can be used for both PCIe and SATA interface.
NVMe supports a whole range of things that wasn't possible with AHCI as it was designed specifically for SSDs. AHCI was designed for spinning platters. That being said, not all PCIe SSDs are NVMe, some are still AHCI.