NVMe - 'non-volatile memory express'. This is a _protocol_ that storage devices like SSDs can use to communicate with the external world. It is orthogonal to whether the disk is attached to your motherboard via pcie, or it lives somewhere else in the datacenter and uses a different transport layer. For example, local NVME SSDs will use PCIe transport. But you can also have NVME-over-TCPIP, or NVME-over-fiber-channel. Or NVME-over-Fabrics. Many of these are able to provide significantly lower latencies than a millisecond.
As a concrete example, AWS `io2-express` has latencies of ~0.25-0.5ms, though i'm not sure which technology it's using.
nvme over fabrics: https://www.techtarget.com/searchstorage/definition/NVMe-ove... many interesting presentations on the official nvme website: https://nvmexpress.org/education/documents-and-videos/presen... aws: https://aws.amazon.com/blogs/storage/achieve-higher-database...