The examples in the answer by Shawn J. Goff are correct, but the explanation is the other way around. Please check:
"The right side of && will only be evaluated if the exit status of the left side is NONZERO. || is the opposite: it will evaluate the right side only if the left side exit status is ZERO. "
PS: I edited three times that answer and someone removed that.
The right side of && will only be evaluated if the exit status of the left side is NONZERO. || is the opposite: it will evaluate the right side only if the left side exit status is ZERO.