External

• Part of the contract’s interface, can only be called from external contracts via transactions.  An external function f cannot be called internally (i.e. f() does not work, but this.f() works).

When would you use External function vs Public function?

• External functions are used in proxy patterns with delegatecall(). If you use a public or internal function instead, it will modify the storage of the implementation contract and lead to unintended behavior.
• You will also declare a functional external when you define it in a interface

Public

Public functions are also part of the contract interface and can be called either internally or via message calls.

Internal

Internal functions can only be accessed from within the current contract or contracts deriving from it. They cannot be accessed externally.

Private

Private functions are like internal ones but they are not visible in derived contracts