Both M.2 and SATA Express allow for PCIe storage.
M.2 replaces mSATA. It ranges from a bit smaller than a SD card, to about 3x the size of an SD card. You need to make sure to get a device that is the right size, and/or see if you can work with changing the placement of the mounting screw.
SATA Express extends SATA, adding PCIe connectors to the works. For client PCs, SATA Express is cumbersome, expensive, and annoying, but provides a fair degree of backwards compatibility. For machines with backplanes, like most servers, it's about the most ideal way imaginable to allow for backwards-compatibility with SATA and SAS.
A SATA drive supporting SATA Express or M.2 will be just as fast as any other. A PCIe SSD over either may be faster, but right now, the degree to which it will be is limited, since it will need a custom driver stack, or sit on AHCI, which adds a couple more bottlenecks on top of the controller and NAND. NVM Express, which will supplant AHCI (at least for SSDs), should allow for much faster PCIe SSDs.
With all these changes happening now, and so many form factors, the industry in a kind of chicken and egg place, where everyone is waiting on everyone else to start coming out with the various bits of hardware en masse. M.2 (SATA) has pretty much already taken over, from a big OEM POV, but there are few consumer options, especially under the 2280 size (80mm long, 22mm wide). At the moment, there's not any particular reason to use either standard, over 2.5" SATA, in a desktop PC.