Q: What is the difference between ‘Buenos días’ and ‘Buen día’?
Not much difference, I would say that it is basically a question of local custom. And, as I generally do in my answers to this type of question, I will try to reflect what people in Spain actually do or say – in practice and everyday life.
Here “buenos días” is standard; if you are relatively familiar with local variations you can occasionally use “buen día”, but it is more uncommon and may sound slightly weird. For example, when entering a room you could say “buen día a todos” (… but “buenos días a todos” would also be perfect). If unsure just stick to “buenos días”.
“Buenos días” is hello (in the morning); “hola, buenos días” is a very standard salutation. As is “adiós, buenos días”, an acceptable and usual way of saying goodbye (also in the morning) – but just “buenos días” would not work as a goodbye.
(Substitute with “tardes” or “noches” for other times of day).