What does it mean when you are playing from a lead sheet and you see two totally different chords, stacked one on top of another?

The chords aren't stacked at all.  There is one line of eight bars of chords, and below that the next eight bars.

The only time I've seen anything like that is when a capo is used and the chord shape and the actual chord have both been shown. For example if the capo was at the third fret:

C

Eb

would show the chord shape was a C shape but with the capo the actual chord was Eb. From what you say though this can't be the case as there would be two sets of chords all trhough the song.

The only other possibility would be slash chords showing the chord and the bass note to be played. For example:

C/E

would mean a C chord with an E bass. But it can't be that either as you say the chords are shown one above the other.

I hope someone more knowledgeable than me can answer your question and explain. I'm interested too.

Added' as Me2 suggests, a picture would be a great help. I think were all just guessing.

Added, but the link you give in a comment is not a "lead sheet". All it shows is two rows of chords, one above the other. You play the first line and then go onto the second line. That's what you do when reading anything.