In my humble opinion, Giygas/Giegue is (or, was) the same species as a starman. In Mother1, he has a strange cat-like form, with arms that look suspiciously similar to starmen. When you take into account that they are both aliens, and starmen are under Giygas/Giegue’s command, it just seems to make sense! (attached: quick interpretation of this idea)
The ‘devil form’ Giygas is the same creature, overcome with anger, grief, and loss. This is somewhat understandable – according to the backstory we were given in Mother1, Giegue was raised by Ninten’s grandparents, George and Maria. George grossly overstepped his boundaries and conducted many PSI experiments on the species, which angered Giegue who was disgusted with man’s greed. George was sent back to earth, and Maria was kept on the spaceship until she passed away. After this, Giegue sets out to invade earth and kidnaps all of the adults throughout the world, presumably because he finds them all disgusting and full of the same greed George was. In the final battle, the three children sing Maria’s lullaby to him, which fills him with grief and causes so much emotional damage that he retreats.
Giegue stays dormant and brooding from 198x to 199x where he is so grossly misshapen from the hatred that he begins to lose his grip on reality and his own physical form, seeking only to gain the power to destroy everything on earth. Giygas becomes so powerful and full of evil thoughts that he is no longer a single being, he is a force of evil which influences any man, creature or otherwise that is weak-minded and open to thoughts of greed.
So, in short – Giygas is the embodiment of evil.
A lot of this is my own interpretation, based on the lore we have been given! Take all of it with a grain of salt.