Unity of Being and Absolute Monism refer to the same concept. There is only ONE Absolute Being in existence. Cosmos including all the physical universes and the infinite number of souls are transformations or internal reflections of this Absolute Being which is also known as Consciousness (Puruśa in Sanskrit).
Shrii Shrii Anandamurti reminded us that Puruśa is the same as Ananda which is the infinite ocean of love and bliss. This is the most important point in my opinion. When we talk about the Unity of Being we often over-intellectualize the concept and we forget the “Divine Love” aspect.
There is a practical reason for trying to understand the Unity of Being and the infinity of Puruśa in terms of Divine Love. Trying to understand the vastness of Puruśa in intellectual terms will eventually drive anyone to insanity.
The intellectual approach to the infinity of Puruśa is not possible because the intellect has to proceed within the mental realm which is vast but not infinite. The mental realm is one of the layers surrounding the life giving, witnessing and substantiating nucleus consciousness (Puruśottoma) of the Cosmos. The creation of Cosmos starts from this nucleus which is formed when a portion of the infinite ocean of Puruśa is qualified (confined, bound, subjectivized). The mental realm is a reflection/transformation of Puruśa, therefore the minds that exist within the mental realm cannot comprehend the higher reality by staying within the sphere of the mental realm. When the nucleus consciousness (soul) identifies itself with the nucleus consciousness of the Cosmos some kind of understanding called Self-realization takes place. There are mind training techniques (spiritual practice) towards that goal but the strongest helper is the feeling of Divine Love. All those mind training techniques are useless when there is no devotional feeling.
Unity of Being is not a dry concept
I would like to remind you about an implication of the concept of Unity of Being. This is to make it clear that the Unity of Being concept is not just dry intellectual discussion.
When we are in pain Parama Puruśa (God) feels our pain because our body is part of his body. When we feel joy he feels our joy. When we have samadhi (ecstatic spiritual experience) He enjoys the same samadhi. When we finally return to the infinite ocean of love and bliss (Ananda) in permanent union (Moksha) Parama Puruśa feels endless bliss.
Shrii Shrii Anandamurti said: “the source of every existence is Ánanda or bliss. Everything originates from nityánanda , remains in liilánanda  and eventually returns back to nityánanda.”
Sufi treatment of the concept
In Sufi metaphysics the Unity of Being is known as Wahdat al-Wujud. Ibn Arabi (1165 – 1245) is often cited as the originator of the concept of Unity of Being but obviously this concept existed since Shiva’s time 7000 years ago. We see the same concept being taught by Tehuti 6000 years ago in Egypt. As a testament to the essence of spiritual philosophy, Ibn Arabi, verified the ancient teachings in his own Self-realization and discovery of the truth and provided sound logical arguments for it.
Ibn Arabi’s concept of “wujud” corresponds to the concept of Brahma inTantra Yoga. In modern spiritual philosophy “Being” is used to refer to Brahma which is a philosophical term that refers to both the Absolute Unmanifested Consciousness (Nirguna Brahma, Infinite Existence, Ein Sof, Absolute Being) and Manifested Consciousness (Saguna Brahma, Reality, Haq, Yah, Living God) states of the “Being.” Wujud literally means “Being.” Wahdat al-Wujud literally means the Unity of Being.
William Chiittick explains Wujud as follows:
“Wujud’s Self-consciousness is nondelimited, while every other consciousness is constrained and confined. On the highest level, wujud is the absolute and nondelimited reality of God, the “Necessary Being” (wājib al-wujud) that cannot not exist. In this sense, wujud designates the Essence of God or of the Real (dhāt al-haqq), the only reality that is real in every respect. On lower levels, wujud is the underlying substance of “everything other than God” (mā siwā Allāh)—which is how Ibn Arabi and others define the “cosmos” or “universe” (al-‘ālam). Hence, in a secondary meaning, the term wujud is used as shorthand to refer to the whole cosmos, to everything that exists. It can also be employed to refer to the existence of each and every thing that is found in the universe.” 
Today, some Sufi Orders, notably the Bektashi sect and the sect of Universal Sufism, place much emphasis on the concept of Unity of Being.
Subtle Difference between Nondualism and Unity of Being
In reference to the non-dualistic teachings of the Upanishads, there is a subtle difference between Nondualism and “Unity of Being” philosophies. In Nondualistic teachings the Cosmos is referred to as illusion. In the “Unity of Being” teachings the Cosmos is not illusion, Cosmos is the relative truth. It is my opinion that Nondualism is essentially the same as “Unity of Being”, and that the word “illusion” was used by the Nondualists to refer to the concept of “relative truth”. I wrote an article called “It is not just semantics” to make a point that words do matter in spiritual philosophy. So, in practice Nondualists and believers of the “Unity of Being” follow the same spiritual path, but when it comes to explaining spiritual philosophy words matter.
Pantheism, Panentheism, and Unity of Being
The English the term Pantheism means All is God while “Unity of Being” emphasizes that there is just a single being in existence and this single being is God. However, “Unity of Being” may be closer to panentheism, because it states that while the Universe is part of God or God’s mind, God is still greater than his creation.
 Literally; ‘nitya’ (eternal). ‘ananda’ (bliss).
 Literally; Cosmic Play or Cosmic Drama
 William Chiittick, “Imaginal Worlds”, (1994), pg.15