The && and || logical operators seem to have more general recognition and background usage, although the and and or form of the same logical operators is taking more and more acceptation for the sake of readability.
So here is a list for the results when evaluating the expressions in PHP. I am sure that this can be applied to a bunch of other languages. (I think it is a little bit superficial to say that it apply to all programming language since I only know some of them).
Logical operator AND (&& )
false and false => false false and true => false true and false => false true and true => true
Logical operator OR (|| )
false or false => false false or true => true true or false => true true or true => true
Logical operator NOT (! )
!false => true !true => false