Can mouth guard for boxing be used for karate, basket balls, etc?
Are they are the same?
No they are not. The mouth guards are designed to protect against different kinds of impact most common to sports.
In summary, use the recommended mouth guard for the sport you want to participate in or need you have. Research and experience goes into the needed mouth protection for each one and the guards are designed specifically for that. There are some variations and min-max protection within the guards, but follow the sport you are after. If all the mouth guard styles are for the same sport/purpose then find what you like best.
Note: There are some mouth guards that say for everything, that is because it's extra protective and they are saying it will work for whatever since it's the max protection design you might need.