In various translations ( chabad, and christians ) they translate it to spirit of Gd.
Since ruach can be a wind, or breath. Why is these terms specifically not used.
How can explain the difference to a person who thinks that this is some manifestation of Gd instead of a different "person" of Gd.
"Spirit" and "wind" are both helpful translations. But in any case the commentators make it clear "the spirit of God" is an emanation from God that proceeds by His command rather than being some "part" of Him.
"וְרוּחַ אֱלֹהִים מְרַחֶפֶת" – כסא הכבוד עומד באוויר, ומרחף עַל פְּנֵי הַמָּיִם ברוח פיו של הקב"ה ובמאמרו, כיונה המרחפת על הקן, אקובטי"ר בלע"ז.
And the spirit of God hovered - the Throne of Glory stands in the air, and hovers over the face of the waters by the spirit of the Holy One's "mouth" and by his word (i.e. by His command), like a dove hovering over its nest. Acouvtir O.F.
And the Targums have "a spirit (of kindness/goodness, rachamim) from before (i.e. emanating from) God."
The Zohar has explanation as both spirit and wind:
"ורוח אלהי"ם", רוח קודשא דנפיק מאלהי"ם חיים, ודא מרחפת על פני המים, בתר דהאי רוח נשיב, אבריר דקיקו חד מגו ההוא פסולת כטיסא דזוהמא, כד אתבריר ואצניף ואצריף זמנא ותרין, עד דאשתאר ההוא זוהמא דלית ביה זוהמא כלל. כד האי תהו אבריר ואצריף, נפיק מניה (מלכים א יט יא) רוח גדולה וחזק מפרק הרים ומשבר סלעים ההוא דחמא אליהו, אבריר בהו ואצריף, ונפק מניה רעש, דכתיב (שם) ואחר הרוח רעש, אבריר חשך ואכליל ברזא דיליה אש, דכתיב ואחר הרעש אש, אבריר רוח ואתכליל ברזא דיליה קול דממה דקה.
Translation:
"And the wind (also: 'spirit') of Elohim" (Ibid.) ALLUDES TO the Holy Spirit (Ruach) that proceeded from living Elohim and "moved over the surface of the waters." THIS MEANS THAT after this wind blew, a thin layer from the refuse was refined, just as the filth flies off and away. In this manner, it was refined, covered and purified over and over again until the foulness was left without any filth.
When this Tohu was refined and purified, "a great and strong wind rent the mountains, and broke the rocks..." (I Melachim 19:11) Then it emerged like the wind that Eliyahu saw. The Bohu was refined and purified and noise came from it, as it is written: "And after the wind an earthquake (also: 'noise')" (Ibid.). When the darkness was refined, fire was then included in its secret, as it is written: "And after the earthquake a fire" (Ibid. 12). The wind was refined and a "still small voice" was included within it. -- Translation of Michael Berg, capital letters are his elucidations
It is possible to translate it as a 'wind from G-d' but as the commentators point out it is not necessarily wind in the way we appreciate it.
The Ibn Ezra there serves as a good introduction and does explain it as some form of wind:
ורוח אלהים. סמך הרוח אל השם בעבור היותו שליח בחפץ השם לייבש המים:
AND THE SPIRIT OF GOD. Ru’ach (wind) is in the construct with Elohim (God) because it was the medium employed by God to dry the land. (Sefaria translation)
However, as the Chizkuni asserts it was something a lot more spiritual and not to be understood in the physical sense:
ורוח אלוקים, “and the spirit of G-d, etc.” This expression too tries to describe for us something that exists outside the “universe” is abstract, similar to the expression תהום, in the first half of this verse. This “רוח” is also perceived as קדש, holy, and is described in the Talmud Chagigah 12 as one of the 10 phenomena that G-d created on the first “day.” (Sefaria translation and additional notation).
The Netziv explains in his HaEmek Davar similarly, that the translation 'wind' would not really be the appropriate in the given context, as it wasn't wind as we know it:
And the spirit/wind of God was hovering upon the face of the waters: It was not blowing strongly in order to dry [the waters,] like other strong winds that are known by the name, spirit/wind of God, but rather it was hovering calmly.
A final point can be brought from Rabbeinu Bachya that this wind was of a more Divine form and thus the translation of 'wind' would not really do it justice:
והרוח מנשבת ותכנס בחשך ותרחף על המים, ומה שאמר ורוח אלהים היה ראוי לומר והרוח אבל ייחס הרוח לשם אלהים
The wind was blowing entering the darkness and hovering above the water. When the Torah speaks of ורוח אלוקים, we would actually have expected ורוח האלוקים, i.e. “the wind (spirit) of G'd;" the reason the Torah chose to omit the letter ה , thereby apparently identifying wind as something divine, this is because of all matters in the physical universe wind is the closest to the invisible abstract force called G'd. (Sefaria translation & notation)
Thus in this context, 'the spirit of G-d' is more fitting.
