Do they, really? I strongly suspect that, if I asked people even in one geographic region, I would get many different descriptions of what that means. And this assumes they belong to the same religion and acknowledge the same god.
To this you can add how they feel about themselves on any given day. A person who considers himself a sinner one day may feel despondent in regards to God. A person who considers himself obedient will feel better about God.
But none of it changes the fact that they will tell you that they feel God in their hearts.
Or how about the person who is inexplicably happy over the loss of someone or something? Or the person who is sad over gaining something and can't tell you why, they just are?
Would we tell them that they are feeling the wrong kind of happy or the wrong kind of sad, and base our argument on testable claims and reliable data?