No it's not the same. For example he sings the line "your makeup running down your face" differently. In the recording "down" is a semitone up from "running", but live he sings the two words on the same note, and then a full tone up on the word "your".
There's a lot of differences in the tonality and head voices. One big reason it sounds VERY similar, is because they produce their own albums, so whatever sound production was on the album, is the exact same on live. They are also using their own/or mostly the same equipment, amps, effects, etc. The primary sound engineer also tours with them, so the production is the exact same. That being said, there is use of playback for harmonies, but the main vocals is live.
