Chemistry - Molten vs Liquid

As you said, the meaning is exactly the same. Molten reduces the ambiguity, because you emphasize that you know, that it is solid substance at laboratory conditions and you heat it to become liquid (while staying pure substance).

As an example, the "electrolysis of liquid sodium chloride" is in principle enough to tell you all about the process, but as we often like to dissolve the salt in water, you might be slightly unsure, whether the meaning is 100% clear. Therefore "electrolysis of molten sodium chloride" is better choice.