Happy New Year Hangul
The first one literally means happy new year while the next one in most cases stands for the same meaning but it actually may you have many blessings or lots of fortune.
Happy new year hangul. One can also write merry christmas in hangul that is 메리 크리스마스. Sae hae haengbokhaseyo 복 많이 받으세요. If you just want to stick to the usual happy new year you can say 행복한 새해 보내세요 haengbokhan saehae bonaeseyo.
This is how you greet this holiday in korean. Merry christmas and happy new year everyone. Haeng bok han sae hae dwe se you polite in hangul.
Somehow this is similar to how we always say have a prosperous new year.
Geon gang ha se yo 건강하세요 means please be healthy so this phrase simply translates to please stay healthy this coming year too. This means to send a happy new year. This is literally translated as to send many new year blessings.
Which means something along the lines of have a happy new year. Or you can say. Bok manhi padeuseyo these are some of handy greetings for new year.