The two trains of FF6 and FF8 are likely unrelated to each other, but it can't hurt to speculate. FF6's Phantom Train carried the dead to the "other side", and caught Cyan and Sabin on the way. It also appears as an optional boss in FF1: Dawn of Souls. In FF8, on the other hand, Doomtrain is a summon which rams into the enemy for Poison damage and causes a variety of status ailments, including the always useful Vit 0.
-Demon Train (Dawn of Souls)
-Ghost Train (NA) / Phantom Train
-Doomtrain (NA) / Grasharaboras (JP)
ATK: Runaway Train