I am told that the original Hebrew or Greek writing of Ephesians 1:26 or Luke 1:28 is important in the use of the word "grace". Unfortunately I do not know if its important because its the same word or if it has different meanings. If someone could tell me any similarities or differences in how this word is used, it would be greatly appreciated. Thank you and God Bless.
Ephesians 1:6 and Luke 1:27, 28 were originally written in koine Greek. That was the popular language in the time and place the New Testament was written, and both Jews and Gentiles could read/write it, hear it, and speak it. Thus, when making parallels using language principles, in order to do so with respect to the context of the passage, look to Greek rather than Hebrew. You can find both Greek and Hebrew translations of both the New and Old Testaments, but to stay true to the text's original meaning it's typically best to look at Hebrew for Old Testament and Greek for New Testament writings.
As for the words translated "Grace" in English versions, there's a few things I see when looking at these verses in my research. Btw, I typically use the English Standard Version for academic research and compare it to the NETBible online for word studies (such as looking up the word "grace" in this case). Then compare those findings to other English translations. Using multiple versions gives the best overall picture of meaning.
Things to note about these two texts in regards to grace (as I saw in the NetBible online):
The word used to mean grace in Ephesians 1:6 is τῆς χάριτος and the phrase its a part of (δόξης τῆς χάριτος αὐτοῦ
can be translated in English as "to the praise of his glorious grace".
In Luke 1:28 - in the Greek text - the word directly translated as "grace" is there but conjugated differently to fit within its context. Instead of χάριτος the word in Greek is κεχαριτωμένη translated as "to peruse with grace, to compass with favor, or honor with blessings"; the NetBible has it translated as "favored one".
According to my limited research, the only connections I see between the two passages regarding grace is that in both cases the source of grace comes from God. In Ephesians, Paul is writing praises to God for his graciousness which comes to us from Jesus. Luke also attributes grace coming from God and being bestowed upon Mary, who was to be the mother of Jesus, a position of great honor according to Jewish culture at the time and also today due to Jesus being Savior of humankind. The texts can not reasonably be used to support theology which makes Mary the source of grace. See NETBible quote, "The address, favored one (a perfect participle, Grk Oh one who is favored) points to Mary as the recipient of Gods grace, not a bestower of it. She is a model saint in this passage, one who willingly receives Gods benefits. The Vulgate rendering full of grace suggests something more of Mary as a bestower of grace, but does not make sense here contextually."