Oh, I found the full article. It's from here:
http://home.earthlink.net/~letrimh/inquiry.htm This is difficult to explain and does not have a clear answer. Let me first dispel a rumour which states that the being atop Terra Tower should rightfully be called the Fused Dragon, or as some say, the Lunar Dragon. I have on good authority statements of those who have played the Japanese version of Chrono Cross citing that the creature is in fact called the Devourer of Time (toki wo kurau mono) . No errors in translation were made, so let us now see why this Dragon God is also referred to as a Time Devourer.
First let us be clear on our definitions. For this piece I will use "Time Devourer" to refer to the Lavos/Schala hybrid found in the Darkness Beyond Time, and "Dragon God" to refer to the Dragonian‘s biological supercomputer. Belthasar tells us that the Dragon God was consumed in the distant past by the Time Devourer. Since the Devourer exists independent of the timeline in which the Dragon God exists we have to find a way to explain how the two came into contact. We also know that the Frozen Flame provides a link to Lavos, or more correctly, the Time Devourer. The hypothesis that is commonly accepted is that when FATE used the Frozen Flame to divide and seal the Dragon God a link was formed between the Dragon and the Devourer. As the two became connected Lavos, in a sense, "devoured" the Dragon God and the two became merged physically. From that point onward the six dragon gods of El Nido were merely temporal projections originating from the Darkness of Time. Because of this they physically existed in both Home and Another Worlds, but by the same token they also did not truly exist there, so to speak. Their true body was apart of the Devourer inside the Darkness of Time. Because they were projections they were not subject to the laws of physics that everything else must obey.
As a result they were not fully confined to any one dimension. It is likely that before the time split of 1010 AD all six dragons resided on El Nido, each to their respective isle. When the dimension became divided the dragons, either by choice or by force, were also divided, three to a world. The dragons also appear to be able to drift between the two dimensions, as seen when the Sky Dragon appeared in the Dead Sea of Home World. Shortly before the dragons merged all six congregated in the skies of Another World.
Now to answer this question. Since the Dragon God eventually became a part of the Time Devourer we can rightfully refer to the "Dragon God" seen in Chrono Cross as being the Time Devourer since by this stage it is only a projection emanating from within the Darkness of Time. Confusing, yes? After the Dragon God is defeated atop Terra Tower it can be seen to fade out of existence temporarily. This is because it does not exist in the dimension in the way Serge does. With its temporal projection destroyed the representation of the Dragon God disappeared. To full destroy the true Time Devourer, the being that absorbed the Dragon God, one must travel to the source: the Darkness of Time. Incidentally, because of their merger the Time Devourer can be seen to have a tail. As neither Lavos or Schala had a tail, many believe this was formed as a result of the consumption of the Dragon God. Note that even though the Dragon God was a projection, it still retained its own will and original personality. It acted on its own desires, not those of Lavos.
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Some things can be argued, but it answeres the question above neatly enough.