How can I differentiate edge case testing, corner case testing, and boundary case testing?

Corner Case Testing: When the system breaks only for a specific valid input

eg:  Imagine a function getcar() that that takes a number and all numbers from 1-5 are valid inputs:

But,

  getcar(wheel=?) function works with all numbers but fails for getcar(wheel=3)

Edge Case Testing:

Here we check that the system handles extreme values of valid limits.

  For the above example, the valid edge case scenarios are getcar(wheel=1) and getcar(wheel=5)

Boundary Case Testing: Here we check that the system handles boundary values around the edge case values. so in the above example, edge case values are 1 and 5. So, the boundary cases would be 0,2,4,6