I can't speak to the Japanese specifics, and I would suggest that that's probably quite relevant here; but in a more general sense, nothing is particularly surprising about what you describe.
Your son is in a new environment, and all changes in environment take time. For all but the most outgoing of people, changing jobs would mean they act significantly less social for a while, as they adjust to the new social environment. This is normal - you're learning what is appropriate and what is not.
For a five year old, it's far bigger of a change - as he doesn't have the context of years to realize people are mostly all the same, and environments are mostly all the same. So he is quieter while he learns to adjust to the new environment.
Some children will react differently - some might be more active, more outgoing, some will be quieter. But it's all how they learn to adjust. Give him some time - my son took several months to adjust to kindergarten, but by the end of the year he was as social as I could reasonably expect.
Over time, as he gets used to it, most likely this will fade and he'll act just as he does with kids at the park. But if it doesn't, you can address it as lessons to be learned, and teach him the importance of greetings - even trivial, unmeant greetings - over time.
At home, don't expect him to discuss his day with you as your wife might. Kids start to develop their own spaces from my experience, and it's normal for them to not really want to discuss school "on demand". Instead, let him open up to you when he wants to. He'll get excited about something and want to tell you - if you're constantly asking him, he'll not do that and instead consider talking about school a chore. I usually ask a "how was your day?" and then leave it alone; when I don't, and push harder, I get less back.
Do talk to the teacher, though, if you're worried about how he's socializing. The teacher can tell you how he's doing with the other kids, and should be able to give you any feedback that's useful for you. This should be a regular thing - check in periodically, not just a five second "how're things going" but a longer conversation, once a month or so in my opinion.