What Does It Mean to Say That the Logos/Word Shares the Father's "Essence"? (Wallace and John 1:1c)

Trinitarians do not propose that the Logos/God the Son is the same person as the Father or the holy spirit (Holy Spirit): the doctrine of the Trinity is often interpreted in this way by friend and foe alike. But the church creeds make it clear that the divine "persons" should not be confounded, nor should the divine substance be divided.

So when Daniel B. Wallace (Greek Grammar Beyond the Basics) asserts that the Logos "shared the essence [nature] of the Father," (based on John 1:1c) he means that the Son is fully God as the Father is fully God, but they're not the same person. Augustine of Hippo discusses this very point in his work De Trinitate.

To word matters another way, Wallace is claiming that the Logos has all of the properties that pertain to Deity; the Word is supposedly Omnipotent, Omniscient, Impassible, Infinite, in short, he is reputedly everything that systematic theologians believe God the Father is. Thus, they claim that the Logos is fully God in this sense, according to John 1:1c. Wallace therefore does not mean what the "person on the street" possibly means when he/she wields the term "essence." Please consult Dana and Mantey for similar language regarding Jn 1:1c.

On the other hand, it appears highly problematic to aver that the Son has every property (P) that the Father does. If the Son and Father share/are the same nature and have every divine property in common, then how could we tell them apart?

Trinitarians obviously appeal to concepts like eternal filiation, eternal spiration or to unbegottenness in the case of the Father, to obviate modalism. However, we must ask whether eternal filiation or spiration are satisfactory approaches and are they scriptural? Moreover, these views evidently presuppose a Platonic schema when it comes to time and divine begettal. However, does not Plato's schema have some logical difficulties?

Charles Ryrie once wrote about the eternal generation doctrine:

“I agree with Buswell (A Systematic Theology of the Christian Religion, pp. 105-12) that generation is not an exegetically based doctrine. The concept it tries to convey, however, is not unscriptural, and certainly the doctrine of sonship is scriptural. The phrase 'eternal generation' is simply an attempt to describe the Father-Son relationship in the Trinity
and, by using the word 'eternal,' protect it from any idea of inequality or temporality. But whether or not one chooses to use the idea of eternal generation, the personal and eternal and coequal relation of the Father and Son must be affirmed.”

Trinitarian Spiros Zodhiates criticizes the eternal generation doctrine because he thinks it is not taught in the Bible. There's also the question of whether eternal generation or spiration strictly conform to the principles of logic: John Feinberg thoroughly examines the (potential) logical merits or demerits of these notions in No One Like Him.