NO......
modulate means to change the key
Transpose is to shift the chord......
For example, let's take Hez's new CD
"And because is the Greatest power, He shall not be defeated" (No Defeat) They are modulating
"Grateful Grateful Grateful Gratefulness" (They are transposing the notes, same key.....the tenors take the altos old note, the altos the old soprano, and sopranos the old tenor an octave up......
HOPE THAT HELPS