Sure an E is an E, but an Eb is not an E. When you change the key the song is in to a lower key, the vocal parts are changed to a lower key as well. Instead of singing a song in the key of B, for example, the song will now be sung in the key of Bb.
+1.
I played with a singer that wanted to play Bon Jovi Livng on a Prayer but the key change at the end is super high. Song is originally in E, we played it in C# and it sounded great. Bass strings were floppy as hell though as I had to tune down 3 semitones.

