• None vs np.nan

The following values are considered false:

• None
• False
• zero of any numeric type, for example, 0, 0L, 0.0, 0j.
• any empty sequence, for example, '', (), [].
• any empty mapping, for example, {}.
• instances of user-defined classes, if the class defines a nonzero() or len() method, when that method returns the integer zero or bool value False. 1 All other values are considered true — so objects of many types are always true.

Source: https://docs.python.org/2/library/stdtypes.html#truth-value-testing

So by these conventions None is False and np.nan is True.

• boolean vs bool

Boolean dtype implements Kleene Logic (sometimes called three-value logic).

Source: https://pandas.pydata.org/docs/user_guide/boolean.html

For example, True | NA gives True because NA can be True or False and in both case the OR operation (|) will result to True because we have at least one True. Similarly, False | NA gives NA because we don't know if there is one True.