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NVMe
A solid-state drive that talks over the fast PCIe bus, usually on an M.2 stick, far quicker than SATA.
A protocol for solid-state drives that communicate over the fast PCIe bus, typically on an M.2 stick, giving much higher sequential speeds than older SATA SSDs. The 'Gen3 / Gen4 / Gen5' label refers to the PCIe generation and roughly tracks the drive's top speed, which has climbed from around 3,500 MB/s on Gen3 to multiple gigabytes per second on Gen4 and Gen5.
Concrete example
an NVMe drive can copy large files far quicker than a SATA SSD, though for everyday app loading the difference between PCIe generations is far smaller.
What it means when you're buying
NVMe is the sensible default for a boot drive, but for most users a good Gen3 or Gen4 drive is plenty — paying up for Gen5 mainly benefits sustained large-file workloads and may need extra cooling.