呢两句恭賀新禧既英文係相同定係唔同 ?

In general, they are the same, but:
Happy New Year - 1st January
Happy Lunar New Year - Happy Chinese New Year.

Lunar means moon, and this is the first day of each month, of a new year.

我地住係外國既中國人﹐係一月一號會同D外國人講﹕ Happy New Year﹗ 因為一月一號係外國人既新一年。

到農曆新年﹐ D外國人會同我地講﹕ Happy Lunar New Year﹗因為農曆新年係中國人既新一年。

用Lunar呢個字係因為呢個字係指月亮。 我地中國人既月曆係跟個月亮變化而形成。 所以咪叫Lunar嚕。