I am talking about the root "AR" not the words aryan or arab.
In terms of religion Prophet Noah (Peace be upon him) had 3 sons, in the order of their birth they are Shem, Ham, & Japheth.
Shem is the father of the Semitic people, as in the original speakers of the Semitic languages. As far as I know the region the Children of Shem originally inhabited is all of Arabia, Syria, Lebanon, Jordan, Iraq, Palestine, Israel & Lebanon.
Arabic is a Semitic language.
Japheth is the father of the Indo-European people as in the original speakers of the Indo-European languages. Keep in mind that even though Indo-European languages are some of the most spoken languages today, not all of the speakers of those languages are the Children of Japheth. This is because of cultural influence causing the spread of languages.
Sanskrit is an Indo-European language, a distant sister language of Ancient Greek & Latin if I am not mistaken. This implies that the original speakers of these languages were most likely distant genetic cousins, similar to how the Ishmaelites & Israelites are genetic cousins that speak sister languages, in this case Arabic & Hebrew.
The similarity between the word Aryan & Arab is just a coincidence caused by the English language. Or why does the word Hebrew not resemble the word Aryan or the word Arab keeping in mind the Arabs are their cousins?
In Arabic, here are the words for both Arab & Hebrew.
Arab عربي This is pronounced as "Erby".
Hebrew عبري This is pronounced as "Ebry".
The word for Aryan is الآرية, its pronunciation is just like the Sanskrit word "Arya".
You can notice in Arabic the words "Erby" & "Ebry" are extremely similar because from what I know they refer to a person named Eber who happens to be the great grandson of Shem & is an ancestor of both the Ishmaelites & Israelites. In Arabic the word for Aryan has a separate sound from the word Arab as compared to English because it lacks the sound of the Arabic letter "ع".
Keep in mind that I might be wrong about this, & if someone has better knowledge on this subject, then they should correct me. Oh yeah the Arabic speakers on this forum should correct me if I made a mistake too.