If you use it as greeting both are correct. Different is if you wanna say something like "today is a good day" = "oggi è un buon giorno" (In this case "buon" is an adjective so it has to be separate )

La parola corretta è Buongiorno (tutto unito) Elisa

Hi Thaynà :) i the first example "buon" is an adjective, and it's used in sentences as "Oggi è un buon giorno per studiare!" - "Today is a good day for studying"; "Buongiorno" is litterally "Good morning" :)) I hope i've helped you! bye!

Both are correct... But the last one is better