In certain contexts, they can be used to mean similar things, but "bother" is a bit of an odd one out here. Bother more often means "to cause trouble or difficulty" than "to cause worry". Trouble/Difficulty: "He never bothers washing his dishes because he expects me to wash them for him." Here "bother" means "to take the trouble" or "to take the time" to wash the dishes. "Don't even bother showing up. You've already missed the party." Here "bother" means "put in the effort" or "to attempt" Bother can also be used a different way which has a more similar definition to worry/concern, but it means something more along the lines of "to upset" or "to annoy" than "to worry". Upset/Annoy: "Does it bother you when I play loud music when you are trying to study?" Here "bother" means "to irritate" "Does it bother you when I make fun of you?" Here "bother" means "to upset" "Does it bother you when I don't come home on time?" Here "bother" does, in fact, mean "to worry" or "to cause concern". As you can see, bother has a lot of different meanings other than worry/concern, so if you are unsure, avoid using bother as a synonym for those two words. I hope this helps :)

Ellos son los mismos. Really, they mean the same. In different parts of the US and in all of the English Speaking world there are different ways to say just about everything. I have learned that in the Spanish world as well. Lots of words for the same thing. Por ejemplo la palabra para butter es mantiquilla. En Paraguay es manteca. You just have to listen where you are and try to use the same speech. No tengo precoupes. No worry or no bother means the same.