What's the difference between material implication and logical implication?
background: I am trying to fully understand the meaning of implication which i understand intuitively . I learned that $P \to Q$ is a connective , which means that $P$ and $Q$ don't have a logical connection or any reason why $P$ being true should MAKE $Q$ be true and it's just a representation of $\neg P \vee Q$ .
question: $P \implies Q$ means that $P \to Q$ is a tautology , what does that mean ? any mathematical examples ?
in other words: What's the difference between $P \to Q$ and $P \implies Q$ ?