Gaëtan / Gaëton as a boys' name is the French form of Gaetano. The meaning of Gaetano is "from Gaeta", and it is the Italian form of Latin Caietanus, referring to a person from Caieta (now Gaeta), a city in southern Italy. According to legend, the place was named after Aeneas' nurse, Caieta, who died there. Caieta may also derive from Kaiadas, a Greek place for the execution of prisoners.
Guy is of Old German origin, and the meaning is "wood, wide". From Wido, which either derives from witu "wood" or wît "wide". It was used by the Normans, and in Old French w- is often converted to gu-. The Normans used forms like Gy and Guido.
The name may also possibly mean Welsh "lively", or Old German "warrior", or from the French guie, meaning "guide, leader".
I agree with Zareza, they are two unrelated names. I'd say that Caietanus, while uncommon, is relatively known in some (mainly Catholic?) countries: Caetano in Portuguese, Cayetano in Spanish, Gaietà in Catalan, Gaëtan in French, Gaetano in Italian, Kajetan in Polish, etc. I don't know of any equivalent in English, but Cajetan seems the common translation for the Venetian saint.
It seems strange to me that Normans also used 'Guido'. It rather looks to me like the typical solution from Wido>Guido in Italian, while the Old French Guy and the Catalan/Occitan Guiu are also expected. Guy in English comes obviously from France as a normal evolution would have given Wede/Weed or Wode/Wood.