"Happy birthday to you" in Korean evolves around "생일 축하해요". The 해요 part is a sentence ending form which can vary depending on how formal, respectul or other things you want to make it.
These four are the most common endings in any situation ('*' marks the the most widely used ones).
* 생일 축하해. To friends or anyone younger, like nephews, nieces, etc.
- 생일 축하한다. Similar, but sounds less friendly and more masculine. Most common betweeen male friends.
* 생일 축하해요[or 축하드려요]. To adults outside of your inner circle (드려요is more respectful than 해요).
- 생일 축하합니다[축하드립니다][. A bit more formal than 축하해요.
하네 in 생일 축하하네 is one of the less common, traditional sentence endings, many of which seem to be dying out now. -네 is an ending used mostly by men to a male friend or other younger men. It sounds authoritative and has a reassuring quality (it is a different one from -네 which expresses a surprise), but it seems to be rare to hear it nowadays. 축하하오 is another old-fashioned one barely surviving among the older generation.