a trail 痕迹 is more impermanent 暂时的, e.g. "I saw a trail of woodchips in the forest." The woodchips could be moved at any time. Similarly, a trail of footprints can be washed away, or simply eroded by time or by other people traversing the same path.

a track 足迹 would be a more defined or permanent 永久的 pathway,

e.g. "I ran four laps on the track at the high school," or "The hobo walked down the track looking for the next train." In both examples, the track is clearly defined。 可以被永恒追踪的足迹。

a trace 踪迹, in my understanding, is not a reference to any sort of path at all, but to some part of a person's belongings or DNA or the like that has been linked to a particular path 特殊的踪迹, e.g. "I smelled a trace of her perfume as I followed her into the alley" or "I found a trace of his pantleg at the crime scene."