History of term
Latin adjective consubstantialis was coined by Tertullian in Against Hermogenes 44, as a translation of the Greek term homoousios. Since the Latin language lacks a present active participle for the verb "to be", Latin authors rendered the Greek noun "ousia" (being) as "substantia" or "essentia", and the Greek adjective "homoousios" (of the same being) as "consubstantialis" or "coessentialis". Unlike the Greek words, which are etymologically related to the Greek verb "to be" and connote one's own personal inherent character, Latin "substantia", connotes matter as much as it connotes being.
The term consubstantial is also used to describe the common humanity which is shared by all human persons. Thus, Jesus Christ is said to be consubstantial with the Father in his divinity and consubstantial with us in his humanity.
It has also been noted that this Greek term "homoousian" or "consubstantial", which Athanasius of Alexandria favored, and was ratified in the Nicene Council and Creed, was actually a term reported to also be used and favored by the Sabellians in their Christology. And it was a term that many followers of Athanasius were actually uneasy about. The "Semi-Arians", in particular, objected to the word "homoousian". Their objection to this term was that it was considered to be un-Scriptural, suspicious, and "of a Sabellian tendency". This was because Sabellius also considered the Father and the Son to be "one substance". Meaning that, to Sabellius, the Father and Son were "one essential Person". This notion, however, was also rejected at the Council of Nicaea, in favor of the Athanasian formulation and creed, of the Father and Son being distinct yet also co-equal, co-eternal, and con-substantial Persons.