All of the terms you mentioned refer to the newest PCIe solid state drives. The major difference is the way they are connected to a motherboard.
SSD's designated as M.2 are PCIe ssd's that are plugged in directly to an M.2 port on the motherboard.
SSD's designated as PCIe are typically M.2 ssd's attached to a PCIe adapter card that is plugged into an appropriate PCIe slot on the motherboard.
SSD's designated as U2 require a special connector. Currently the only consumer ssd using the U2 connector is the Intel 750. The U2 connector is not popular with consumers.
NVME refers to a communications interface/protocol developed for SSDs by an international consortium of vendors including Intel, Samsung, Sandisk, Dell, and Seagate. The...