Nintendo has confirmed that OoT Link is the Hero's Shade (Hyrule Historia), plus the Skull Kids are afraid of adults (as said by Navi in OoT), meaning the kokiri turn into Skull Kids (Link is not Kokiri but Hylian). I also think that somewhere in OoT it said that Kokiri turn into skull kids if they get lost in the Lost Woods while Hylians, young or old, turn into Stalfos and Stalchildren if they get lost in the Lost Woods.
^ This. Also the Skull Kid of
Twilight Princess is likely a 'remnant' from the past (
Ocarina of Time), or the Skull Kid to whom the Hero of Time taught Saria's Song (we'll call him the "OoTSK"). Keep in mind it has been HIGHLY
suggested that OoTSK and the Skull Kid of
Majora's Mask are one and the same; though I'm not absolutely sure this has been confirmed. With that exists a minor, albeit indirect connection of
MM with
TP. Anyway... If he's not the "OoTSK", then he could simply be one of those other Skull Kids from
OoT who probably just listened to Hero of Time play his various tunes during his travels through the Lost Woods and learned them by ear. I've also surmised the possibility that
TP's Skull Kid may not be directly from
OoT/
MM at all. Instead he could be a somewhat metaphysical being - sent by divine intervention by the Goddesses to aid TP Link on his quest - that takes the form of a Skull Kid for whichever reasons. There might also exist the possibility that he's the spiritual manifestation of the OoTSK. In any case, the minor differences in appearance might have to do with the art/graphical direction between the two games -
OoT and
TP, and possibly other factors.
Note: Some theorists have noticed a slight similarity between the face of the TP Skull Kid and the Moon of MM. Of course, said theorists could be delving too much into things, and if any similarities between them exist at all, it could be an Easter Egg or reference of sorts. However, I find those similarities interesting nonetheless. :yes: