You're not the very first person to have noticed a resemblance between these two characters. Upon the reveal of Gaepora,
tons of
posts containing theories involving he and Rauru started showing, in an attempt at finding a connection.
Many fans had suspected that the Owl, Kaepora Gaebora, that guides Link in Ocarina of Time is Rauru in disguise. For a time there was not very much to work off of, aside from rumors from two Gossip Stones:
Gossip Stones (Ocarina of Time) said:
"The owl named Kaepora Gaebora is the reincarnation of an ancient Sage."
"They say that strange owl, Kaepora Gaebora, may look big and heavy, but its character is rather light hearted."
Over time, such theories remained prominent, that is, until SS came along. Upon seeing Gaepora, many fans believed Rauru was going to appear in
Skyward Sword (before his real name was revealed). Posts were flying in. Along with his name, several things were revealed: It was confirmed that he is the Headmaster of the Knight Academy, Zelda's father, and that he gives Link the green garb upon passing the flight exam. Nothing connecting him to Rauru or the owl was mentioned. There was not a single in-game hint of a connection aside from his resemblance to Rauru.
Unfortunately, no connection between these two characters has been confirmed, not even in
Hyrule Historia. What
Hyrule Historia does unveil is the truth behind the mystery of the Kaepora Gaebora's (the owl from OoT) identity. What was confirmed is that he was indeed Rauru in disguise; the owl was the form that he took outside of the Sacred Realm. The same source claims that no connection between Rauru and Gaepora exist, aside from a similar appearance, which was a reference that was thrown in SS to commemorate Rauru.
Slightly off-topic: One thing's for certain is that Rauru was alive sometime around the era of SS [before or after], as it was he [and others] who built the Temple of Time over the ruins of the Sealed Temple. It seems that he remained dormant in the Sacred Realm most of the time. If anything, Gaepora's parents may have known of Rauru through legends passed down by the elders, and named him in honor of Rauru. However, a sort of "vice-versa" scenario might come into play there. To the point: They are not one and the same, and no confirmed connection exists between the two.
Dunno why I'm posting this here, but meh...
Hyrule Historia (Shogakukan) said:
"ラウル: 古の時代、時の神殿を造った賢者。リンクがマスターソードを抜前は、怪鳥ゲポラ・ゲボラとしてその冒険を見守っていた。 Rauru: He’s the sage who built the Temple of Time in ancient times. Before Link pulled the Master Sword out, he followed Link’s adventures as the owl Kaepora Gaebora.