Ghirahim it seems is composed of many things that make Fi, he's basically a proverbial "Dark Fi" in a sense. However, if you noticed, Demise pulled the sword out of Ghirahim as opposed to Fi appearing from the Master Sword. But it's obvious that these two are not of the same group. Fi was created by Hylia to aid the chosen hero - Link in this case - and Ghirahim is part of the Demon Horde. Ghirahim is undoubtedly not made by the Goddess, and his mannerisms are not at all similar to that of Fi's. He is emotionally unstable whereas Fi is robotic and lacks any real emotion. I think from this we can conclude that although made similar, the two were created by opposing forces; perhaps Ghirahim was made by Demise himself.
Now, I think we should take a step back and compare the two swords, Fi and Ghirahim.
This is the True Master Sword, received upon defeating the Imprisoned for the second time. Take notice of the Triforce emblem imbued into the bottom of the blade. This is a very well-known thing on the Master Sword; it has been imprinted upon the sword since Ocarina of Time. A yellow gemstone is also found on the handle right before the blade itself. The blue of the handle and the white of the blade mesh together perfectly; distinguishing both parts of the sword but creating an ornate and decorative design to the sword. The sides of the handle that jut out curve up slightly and have three small parts connected to each other; small lines separating them all.
And then there is Demise's blade. Take notice of the similarities between it and the True Master Sword. A Triforce symbol is also placed onto the blade. In contrast to the Master Sword's yellow gem, Demise's "Anti-Master Sword" has a red gemstone, giving it a much more sinister look than the Master Sword could ever appear. Unlike the Master Sword, the colors of the handle and the blade mesh together, creating a sword that appears to just be a blade. The blood-red is a contrast to the Master Sword's blue. The connected lines on the jutted ends of the handle in Demise's sword are more prominent and are only connected around their base; making them appear almost like claws. The smoothness of the Master Sword's blade is lost with Demise's. Jagged edges create a threatening-looking blade that looks painful just to touch.
Now, these two swords have opposite ends of the spectrum in their design choices, but they are very similar, quite like Fi and Ghirahim are. Like the two sword entities, they have their similarities and their obvious differences. I would never say either the blade nor their spirits are created by the same force. Perhaps Ghirahim was created by Demise to act as his blade, but gave it a life of its own in the event of Demise being defeated like he inevitably was.
Fi's creation was to aid Link, so why can't Ghirahim be created to aid Demise? It seems Demise contains God-like power, able to badly wound Hylia. Even his sword is powerful enough to do great damage to the Water Dragon. I don't see who else aside from Demise could even forge such a powerful weapon. Hylia would never create such a deranged adversary that could snap so easily and go on a rampage of sorts - perhaps that's why she made Fi so emotionally inept.
Ghirahim being created by Demise would make sense why Ghirahim called him Master. If you noticed, when Ghirahim bowed before Demise - I believe Fi curtsied at Link, calling him Master when she first met him - and called him Master, it was highlighted in blue, which was never done before in the game. There's significant reason why that happened; he's his Master because Demise is his creator. Demise's great power with Ghirahim is almost unnatural. It's as if Ghirahim was created
for him, and perhaps Ghirahim actually was. Ghirahim didn't pursue Zelda for any reason other than to capture her. Had he not needed to resurrect Demise, Ghirahim would have never even looked at Zelda twice. She would have been useless to him.
