Happy Birthday in Japanese?

Question:

I always thought it was
おたんじょうびおめでとうございます
(otanjoubi omedetou gozaimasu)
Or similar, shorter forms, depending on your level of familiarity

And then somebody told me that the Japanese don't use "Happy Birthday", or a similar phrase like we do for birthdays, but have a different way of wishing them well.

I posted an almost identical question a day or so ago, yet again got two conflicting answers. I've been confused for a little while...

If my belief is correct, and uhm... I wanted to send some fan-mail to a favourite Japanese celebrity of mine (Camui Gackt) for his birthday, which form of (o)tanjoubi omedetou (gozaimasu) should I use, so as to not seem rude?

Answer:

We use おたんじょうびおめでとう.

If you use ございます, it would sound too formal. Unless you say it to your boss or someone like that, you don't need to use it.