What is a NVMe SSD?
A NVMe SSD is a solid state drive (SSD) that is plugged directly into the PCIe port on the motherboard instead of being connected to the SATA port via cable. More specifically, it's a SSD that uses a technology called NVMe.

Quotes
The NVMe's website states:
NVMe is widely considered the defacto industry standard for PCIe SSDs
https://nvmexpress.org/about/ (accessed 2025-01-18)
This means that there COULD be other standards for utilizing an SSD over PCIe. I don't know what they would be, but it's possible for them to co-exist with NVMe. In other words, NVMe doesn't mean just "a SSD that connects to PCIe," it means a SSD that connects to PCIe is a very specific way described by the NVMe specification.
Observations
The PCIe port is also called PCI Express. NVMe stands for NVM Express. NVM stands for Non-Volatile Memory. That's kind of weird because then when we put it together we get "Non-Volatile Memory Express" which doesn't really mean anything.
Non-volatile memory is just any memory where files can be saved "permanently," such as a hard disk drive, solid state drive, thumb drive, a floppy disk, etc. This contrasts with RAM, which is considered volatile memory.
Note: if you ever struggle to remember whether it's NVMe or NMVe, just remember it stands for non-volatile memory. Simple, right?
It seems the real name of the technology employed in these SSDs is "Non-Volatile Memory Host Controller Interface Specification," or NVMHCIS. Essentially, this specification would specify how something that provides non-volatile memory like a HDD would work if we connected it to a PCIe port. As far as I know the only thing NVMe we can buy are SSDs, but theoretically you could make a NVMe floppy disk drive work if you followed the specification.