Are Slotted and Castle Nuts the same thing?
The answer is no they are not the same, but they do serve the same purpose.
They are both used in conjunction with a split pin (cotter pin) to prevent loosening. Used in both low torque situations, e.g. trailer wheel axles, or on critical components where coming loose is not an option e.g. axle nuts on motorcycles.
The difference between the two nuts is the height of the nut. Castle nuts are taller than slot nuts for the same given thread size.
If you can imagine a standard nut with slots cut to approx. 1/3 depth of the nut then you have a Slot nut.
A Castle nut is more of a standard nut with the slotted section "tacked" on the top.
Castle nuts also often have the slotted section of the nut rounded so that a split pin can be confined to closer margins of the nut itself.
The nut can be either tightened to its correct torque and then a hole drilled radially though the shaft and a split pin used to prevent further rotation or in the case of a shaft with a predrilled hole, the nut is tightened to the correct torque and then adjusted slightly so that a slot on the nut aligns with the hole in the shaft. As is the case with trailer wheel nuts.