Why is one force called the strong force and the other one called the weak force?

Answer 1

The strong force is the strongest of the four forces, around 100 times stronger than the electromagnetic force. There's no other reason for the name.

Similarly, the weak force is weak in comparison to the strong force and electromagnetism. It is, however, much stronger than gravity.

These forces are named in contrast to each other because they are both observed at the atomic scale; physicists saw two "nuclear forces" and described one as weak and one as strong. Needless to say, they were rather less imaginative than the people who named gravity and electromagnetism.

Answer 2

The strong force is called strong because it is the strongest of the four fundamental forces, binding particles together inside atomic nuclei. The weak force is called weak because it is much weaker than the strong force and is responsible for mediating processes like radioactive decay.