A math problem can be hard, tough, and difficult. This says that it will take more work to solve. A rock is hard, and a sponge is soft. You can have a tough piece of meat (making it not easy to chew) or a tender piece of meat (making it easy to chew, or "melt in your mouth") Difficult and Hard can be interchangeable I feel. Hard is more colloquial than Difficult. I would use Difficult in a more professional setting, and Hard in a casual setting.

Hard can mean not soft. Tough can mean hard to break. Difficult means hard to solve or hard to please. You are hard on someone if you treat them somewhat unfairly. You are tough on them if you are strict. So there are differences you understand after seeing them used in different contexts. You can see that English is hard. However, it is not difficult to learn because you are tough.