Well, Chrono Trigger, despite being on the DS, is closer to the "Advance" series of the FF games than it is the 2 DS remakes (FF3 and FF4)
Its the same game, more or less, just with some added features here and there. The core game is more or less unchanged barring a few minor things here and there (FF1 is probably the most drastic of a change, due to the job rebalancing and what not, but lets not get into that. Still falls into the "Advance" series)
FF4DS is a straight up full fledged remake. Its the same game in terms of plot and dungeon design, but the mechanics, gameplay, etc. are all changed drastically. Its like a completely new game that has the same plot, characters, etc. as FF4.
If you want to play FF4, I recommend FF4 PSP if you have a PSP. same game but with better graphics, bangs out kinks in the game like bugs, and I believe it upgrades the music, at least instrumentally. It also has all the bonus content of the GBA version.
EDIT: Oh yeah! Further proof that CT is more like the "Advance" series than the DS series:
CT DS was made by TOSE, which also made both the PSX ports and the FF "Advance" series.
FF3 and FF4DS were made by Matrix software.
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