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Answer:
Homoousios and homoiousios are Greek terms used to describe the divinity of the Son in the Trinity.
Homoousios (homoousion) is the term used by the Council of Nicea. It means “same essence” or “same substance.” It means that the Son is of the same essence/substance as the Father and thus is co-eternal and co-equal with the Father.
Homoiousios is the term used by Arians and other heresies that deny that the Son is co-eternal and co-equal to the Father. This term means “of similar substance.” It was used by those who believed that Jesus was “adopted” as a “Son of God” or that he was created by the Father as a being greater than the angels but lesser than the Father.
On a side note, notice that the difference between the spelling of the two words is the letter i, or iota in Greek. Some think that this is the origin of the expression “not one iota of difference” as an expression of sameness.