The verb “to emote” derives from “emotion”, but with a slight change in emphasis. Merriam-Webster says it means “to express emotion,” then adds “in a very dramatic or obvious way”.
That gets to the root of it. Emotions are spontaneous. Emoting is calculated. Emotions are genuine. Displaying them for others may easily become just a pose.
We’ve all seen actors or singers apparently in the grip of deep feelings of angst, joy or sorrow. A moment’s consideration reminds us they are only doing a job. The singer has probably performed this tune hundreds of times. It is impossible she’s feeling the lyrics the way she appears to be, as she might have the first time she sang them. She’s selling the song for the benefit of her audience, and may feel nothing at all.