Stover lock nut is a lock nut that is a bit oval in it's internal diameter. This will give resistance when screwing it into place and make it lock. This is the all-metal alternative to a nylon lock nut.
Also known as K-Nut, Keps nuts are the fusion of a tooth lockwasher and a regular hex nut. When screwing it into place, the "tooths" under it that are a bit in angle will create a resistance and will help the nut from loosing over time.
It's also known as Slotted nut.
The bolt or axle has holes drilled through its threaded end. The nut is torqued properly and then, the nut is rotated forward to the nearest slot. The nut is then secured with something in it.
Square nuts are an alternative to hex nuts. Those are not commonly used and will be required on specific projects when a regular hex nut can't fit. Most of the time, this is a question of lack of space.