Check out the difference between and and &&. In the examples you give the method puts is called without parens around it’s arguments and the difference in precedence changes how it is parsed.
In test 1 && has higher precedence than the method call. So what’s actually happening is puts('hello' && return). Arguments are always evaluated before the methods they’re called with — so we first evaluate 'hello' && return. Since 'hello' is truthy the boolean does not short circuit and return is evaluated. When return we exit the method without doing anything else: so nothing is ever logged and the second line isn’t run.
In test 2 and has a lower precedence than the method call. So what happens is puts('hello') and return. The puts method logs what is passed to it and then returns nil. nil is a falsey value so the and expression short circuits and the return expression is never evaluated. We just move to the second line where puts 'world' is run.