Tantra ritual - mystical contact with deities
Ritual tantric theurgia, like pudja and manasika-pudja, is a traditional way of establishing a telepathic communication with gods and siddhs that is accepted in tantrism. It's an entrance to their levels; a contact with a higher mind. Those who perform rituals are the divine contactors, or mediums, and their rituals are always meditations.
The energy of a mantra, badzhan, and yantra smoothly flows through you, and you softly direct it through visualization or contemplation toward the summoned deity. The deity responds and starts talking to you, but not always as you expect it.
Tavmaturgic ritual is the system of telepathic communication, telepathic contact, the invitation of a deity to visit our private world to establish a communication for own happiness. It's as if a person has invited a very important visitor to his home and tries to entertain him in every possible way, so the visitor may help him to solve a problem, offer a solution, protect from bad people, or help with money.
Theurgia - tantric sadhana of worshiping.
Teurgia is something else. We don't ask the deity about anything specific in this world, but we invite the deity for the sake of the deity himself, rather of for the sake of something else. When deity descends, it's already a blessing if we are opened to it. We become one with the deity, taking his energy in through ourselves. If we ask for something, we ask for the same faith, wisdom of purity, strength of mind, and fidelity that the deity has; Nothing else. We surrender to the benevolence of a deity in order to become one ourself. Deities never ask anything for themselves because all of them are modeled in perfection…
(materials base on satsang of Guru Swami Vishnudevananda Giri).