When you jump, you lift both legs off the ground at the same time. When you hop, you lift either leg off the ground but not both. "Both" is similar to "all" e.g. Which film do you like? I like both of them (2 choices). I like all of them (>2 choices) "Either" is similar to "any". e.g. Which film do you like? I don't like either of them (2 choices). I don't like any of them (>2 choices

"Both ways" means that there are two ways of doing something. Or there are two things to be considered. For example: "Both ways of going to the airport will be fast." "Both ways of doing this project will lead you to a good result." "Either way" is used with no 's' at the end of way. It means one way or the other is considered. "You can eat this cake now or later but either way, you will gain weight." "You can choose to ignore him or reply to his message, either way he will still be mad."