What is the difference between like to and want to?

The difference is desire. "I like to eat octopus Sandwiches" means that you would enjoy one if one were served to you, but not that you have a desire at this moment to get one. But if you say "I want to eat an octopus sandwich" it means that you have a desire to jump in the car RIGHT NOW and go over to Octopus King and get a Big Ock with double cheese. Even if there were no action you could take to get that sandwich, you would take it if you could.