Omnipresence is generally defined within Western Christianity as:
the property of being present anywhere and everywhere. The term omnipresence is most often used in a religious context as an attribute of a deity or supreme being, while the term ubiquity is generally used to describe something "existing or being everywhere at the same time, constantly encountered, widespread, common". Ubiquitous can also be used as a synonym for words like worldwide, universal, global, pervasive, all over the place. The omnipresence of a supreme being is conceived differently by different religious systems. In monotheistic beliefs like Christianity, and Judaism the divine and the universe are separate, but the divine is present everywhere. - https://en.wikipedia.org/wiki/Omnipresence
God remains transcendent to His creation and yet is immanent in relating to it. He can act within creation anytime and everywhere, whatever he wants: He cannot be excluded from any location or object in creation. God is omnipresent in a way that he is able to interact with his creation however he chooses, and is the very essence of his creation. In other words, without God's omnipresence there would be no creation as it currently stands.
God then, being omnipresent, is ontologically different (outside of or other than) the universe but is present any and everywhere within the universe. This is to be distinguished from pantheism where God and the universe are indistinct. Terms that we use to describe space/time are limited in their ability to fully encapsulate what is meant by the omnipresence of God.
omnipresence doesn't mean divine occupation of all space, nor divine distribution over all space, nor indwelling of every entity, nor that God cannot move in space, nor the divinification of the universe; but means that God is fully present every-where, and that God can do different things at different places at the same time. - Domenic Marbaniang, "Omnipresence", Light of Life, Mumbai, February 2018
David, in Psalm 139, expresses what each Western Christian everywhere can say at all times:
Where can I go from Your Spirit? Or where can I flee from Your presence? If I ascend into heaven, You are there; If I make my bed in hell, behold, You are there. If I take the wings of the morning, And dwell in the uttermost parts of the sea, Even there Your hand shall lead me, And Your right hand shall hold me. If I say, “Surely the darkness shall fall on me,” Even the night shall be light about me; Indeed, the darkness shall not hide from You, But the night shines as the day; The darkness and the light are both alike to You.
Part of the Western Christian concept of God's omnipresence is (to quote the Highlander) "There can be only One": The God who "fills all in all" does not leave room for another to also fill all in all. LDS, on the other hand, posits an unknowable number of Gods who already are and who are yet to be.
Does the LDS Church have a similar concept of the omnipresence of God? What, if any, are the differences?