Is there a difference between isset and !empty. If I do this double boolean check, is it correct this way or redundant? and is there a shorter way
This is completely redundant. empty is more or less shorthand for !isset($foo) || !$foo, and !empty is analogous to isset($foo) && $foo. I.e. empty does the reverse thing of isset plus an additional check for the truthiness of a value.
Or in other words, empty is the same as !$foo, but doesn't throw warnings if the variable doesn't exist. That's the main point of this function: do a boolean comparison without worrying about the variable being set.
The manual puts it like this:
empty()is the opposite of(boolean) var, except that no warning is generated when the variable is not set.
You can simply use !empty($vars[1]) here.