I think that this English translation of Onkelos doesn't exactly represent the different words clearly. Onkelos' גִּבָּרַיָּא is both the cognate and translation of the Hebrew word הַגִּבֹּרִים, "the mighty," which includes but isn't limited to giants. The English translation confusingly renders this word as "giants" and then translates רַבְרְבַיָּא as "mighty." רַבְרְבַיָּא would be better translated as "great ones" (e.g. in Deut. 9:1 רַבְרְבִין = גְּדֹלִים). In this verse, Onkelos translates הָאֱלֹהִים "gods" as רַבְרְבַיָּא "great ones," which he customarily does in order to avoid using the word "god" about humans (e.g. Genesis 3:5). So there is really no question why Onkelos renders הַגִּבֹּרִים as גִּבָּרַיָּא since they both mean "mighty."
The question remains, why does Onkelos use גִּבָּרַיָּא "mighty" in this verse both to translate Hebrew הַנְּפִלִים and הַגִּבֹּרִים? I think the answer is clear from the verse itself, as Onkelos read it, which is again obfuscated by translation.
The text of Onkelos that you give has וִילִידָן לְהוֹן אִנוּן גִּבָּרַיָּא. Your English translation gives "there were born from them giants," or using my translation of the word, "there were born from them mighty ones." The word אִנוּן is left out of the English. אִנוּן can mean "those" ("there were born from them those mighty ones"), but the problem with this interpretation is that וִילִידָן is feminine and גִּבָּרַיָּא is masculine, so it can't be the giants who are born. A better translation is probably "there were born from them; they are the mighty ones." So it seems clear that Onkelos, like the Masoretic cantillation, read the end of the verse as "they are the mighty ones."
The Hebrew הַנְּפִלִים "nephilim" is a rare word, and it seems that Onkelos didn't have an Aramaic equivalent for it (the same way that some modern translations have to resort to transliterating the word as "nephilim"; for Onkelos transliteration wasn't a good option because נפילין in Aramaic already has another meaning, "fallen ones"). So in order to interpret what the nephilim were, Onkelos used the verse's own statement as a definition, they are the mighty ones, and therefore interpreted the nephilim in the first instance as mighty ones.
So Onkelos does identify the nephilim with gibborim. That alone doesn't necessarily mean he identifies two species of giant as the same species; he could just be applying "mighty" as an adjective to the giants: גִּבָּרַיָּא means both "mighty" and "giant." But in Numbers 13, he consistently translates Hebrew עֲנָק "giant" as גִּבָּרָא "mighty/giant" until 13:33 הַנְּפִילִ֛ים בְּנֵ֥י עֲנָ֖ק "nephilim sons of giants" which he translates as גִּבָּרַיָּא בְּנֵי עֲנָק "mighty ones/giants sons of Anak" (changing עֲנָק to a proper name). Given that he had used גִּבָּרָא up until then to mean giant, it seems likely that here in Genesis he also meant to use the same word גִּבָּרָא to imply that the nephilim and gibborim of Genesis are the same giants.
* However, a different (Yemenite) version of Onkelos has וְיָלְדָן "they gave birth" instead of וִילִידָן "there were born," which is closer to the Hebrew construction and requires no agreement with gender. So it's possibly grammatical to read this version as "and they gave birth to those mighty ones." However, I think that this doesn't contradict the fact that Onkelos interpreted the verse as saying that they are the mighty ones, as evidenced by the fact that he translates the two words identically.