Some Panentheists believe that the world is God's body, and this is known as Panpsychism meaning all-soul, or everything exists is the body or soul of God. Panentheism is different than Pantheism, in that it still maintains a distinction between God and Creation. In Pantheism, there is an identity between God and all things that exist. In Panentheism, all things that exist are within God and exist as emanations from God or their true subsistence is based in the Divine Nature, yet at the same time God is different, above and over all that is within Him. Some Panenthiests therefore talk about the universe or the world being God's body.
Panentheism as a term was not used more than fifty years ago. Most discussions of Panentheism were muddied in with the all-inclusive pejorative term Pantheism. (For instance, even Atheistic Materialism is a form of Pantheism.) Although the term "Panentheism" is new, the ideas are not but unfortunately, finding clear discussions about Panentheism that are distinct from Pantheism is often difficult to find. One example I've come across is in Charles Hodge's Systematic Theology.
Hodge uses the word "Hylozoism" which is similar to Panentheism with Panpsychism. Hylozoism considers all matter as life, so its a very similar term to Panpsychism where all existence is the living body of God. Like Jonathan Edwards, not all Panentheists clearly affirm panpsychism. For instance, a Panentheist may say that a rock is not considered to be alive even though it is inside God, where other Panpsychist Panentheists would say that rocks are alive because they are a part of the universe which is God's living body (or soul).
Here are two quotations from Charles Hodge where Hylozoism is discussed in a way that is synonymous to Panentheism and possibly with Panpsychism included, yet Hodge is still able to discuss Hylozoism (or Panentheism) in clear distinction from Deism and Pantheism.
§ 3. Hylozoism.
Hylozoism, from ὕλη, matter, and ζωή, life, is properly the doctrine that matter is endued with life. And this is the form in which the doctrine was held by many of its advocates. All matter, and every particle of matter, besides its physical properties, has a principle of life in itself, which precludes the necessity of assuming any other cause for the phenomena of life exhibited in the world. In this form Hylozoism does not differ from Materialism.
Most commonly, however, the term is used to designate a system which admits a distinction between mind and matter, but considers them as intimately and inseparably united, as the soul and body in man. God, according to this view, is the soul of the world; an intelligent power everywhere present, to which are to be referred all the manifestations of design in the external world, and all the activity of the human soul. The relation, however, of the soul to the body, is a very imperfect illustration of the relation of God to the world according to the hylozoistic system. The soul is really exterior to the body, and independent of it, at least for its existence and activity. It is not the life of the body. It neither fashions nor preserves it. It is not even conscious of the vital activity by which the body is developed and sustained. Whereas according to the hylozoistic theory, the soul of the world is its plastic principle, the inward source of all its organizations and of all its activities.
The leading principles of this theory as developed by the Stoics are,
(1.) There are two constituent principles of the universe, one active, the other passive. The passive principle is matter, without form and without properties, i.e., inert. The active principle is mind, dwelling in matter its organizing formative power, i.e., God.
(2.) The universe is therefore to be viewed under three aspects: (a.) As the all-forming power; the natura naturans, or, ἡ φύσις τεχνική. (b.) The world as formed by this living, inward principle. The living κόσμος, or natura naturata. (c.) The identity of the two, as they form one whole. It is only by an act of the mind that the one is distinguished from the other. Therefore the world, as including both, or as the identity of both, is formed with the greatest wisdom, and by a necessary process, for the laws of nature are the laws of reason. Cicero, expounding this system, says, “Natura, non artificiosa solum, sed plane artifex ab eodem Zenone dicitur; consultrix, et provida utilitatum opportunitatumque omnium. Censet [Zeno] enim artis maxime proprium est creare et gignere, quodque in operibus nostrarum artium manus officiet id multo artificiosius naturam officere." [Nature, none of this artificial only, but clearly from the same Zeno is said to be an artist; consultrix, and in providing for its use and purpose of all things. Opinion [Zeno] for the art of it is proper to create and generate most of all, and that of our arts in the works of the hands of a much greater art to officiate a function of nature. -Google Translate] (De Natura Deorum, ii. 22, p. 1116, edit. Leipzig, 1850.)
(3.) The universe, therefore (The All-one), of which God is the soul and Nature the body, is living, immortal, rational, and perfect (ζῶον ἀθάνατον, λογικὸν, τέλειον). God, as the controlling, operative principle in all things, acts according to necessary although rational laws. (4.) The souls of men are of the same nature with the soul of the world, but as individual existences, passing away when the life of the body ceases. (5.) The highest end of life is virtue; and virtue is living according to reason. (See Rixner’s Geschichte der Philosophie, vol. i. sect. 120.)
This system in one of its forms is nearly identical with Materialism, and in the other with Pantheism. There is no personal God to whom we are responsible, no freedom of the will; therefore, no sin, and no conscious existence after death.
- Charles Hodge, Systematic Theology: Volume 1, I.iii.3, pg 245-246,
If, therefore, a divine essence, infinite, eternal, and unchangeable, exists, this essence existed before and independent of the world. It follows also that the essence of God is distinct from the world The Scriptural doctrine of God is consequently opposed to the several forms of error already mentioned; to Hylozoism, which assumes that God, like man, is a composite being, the world being to Him what the body is to us; to Materialism, which denies the existence of any spiritual substance, and affirms that the material alone is real; to extreme Idealism, which denies not only the reality of the internal world, but all real objective existence, and affirms that the subjective alone is real; to Pantheism, which either makes the world the existence form of God, or, denying the reality of the world, makes God the only real existence. That is, it either makes nature God, or, denying nature, makes God everything.
- Charles Hodge, Systematic Theology: Volume 1, I.v.1, pg 368,