M.2 is a socket type. It’s essentially a connector.
PCI-E is a set of CPU lanes to allow your computer to access connections through something you plug into it. This can be a graphics card, a sound card, SSD, or other related hardware.
NVMe is a standard for SSDs NVMe, short for Non-Volatile Memory Express. NVMe is built specifically for SSDs and PCIe as software interfaces usually live for at least a decade before being replaced, NVMe was designed to be capable of meeting the industry needs as we move to future memory technologies (i.e. we'll likely see RRAM and MRAM enter the storage market before 2020).
AHCI (Advanced Host Controller Interface) dates back to 2004 and was designed with hard drives in mind. While that doesn't rule out SSDs, AHCI is more optimized for high latency rotating media than low latency non-volatile storage. As a result AHCI can't take full advantage of SSDs and since the future is in non-volatile storage (like NAND and MRAM), the industry had to develop a software interface that abolishes the limits of AHCI.
SATA III is a different standard for hard disks. Originally designed for HDDs, but adapted for use with SSDs. NVMe is faster than SATA III by about 4x. SATA III SSDs can use an M.2 or SATA connection, depending on the drive.
It’s also worth noting that while an NVMe SSD is theoretically faster than a SATA III SSD by about 4x, in the real world performance is much slimmer. While I have no experience myself with an NVMe drive, my Windows 10 SATA III SSD boots in about 6 seconds. I’ve heard it’s slightly under 4 seconds for NVMe. That’s very little noticeable difference, but enough to make it worth it for some.
Another important improvement is support for multiple queues and higher queue depths. Multiple queues ensure that the CPU can be used to its full potential and that the IOPS is not bottlenecked by single core limitation.
Enterprise is the biggest beneficiary of NVMe because the workloads are so much heavier and SATA/AHCI can't provide the necessary performance.
Source : http://www.anandtech.com/show/7843/testing-sata-express-with-asus/4