The feeling of God's prescence isn't like any of those other feelings you mentioned. It's realy a belief in the prescence of a loving God which then leads to the normal human feelings that you get when believing yourself to be loved ie peace joy and love in return.

The belief, ie the gift of faith, usually comes about after a person opens their life up to the possibility that there may actually be a loving God that wants to know and live in them. Then after a prayer, at some point, faith is experienced as a gift and not something that the individual has brought upon themselves. It is not a temporary feeling but something much deeper and enduring.