1.
New Year's Day; the morning of January 1st
Strictly refers to the morning of January 1st, though in modern usage it is often used to mean all of January 1st. The character 旦 originally means dawn or morning.
元旦 strictly refers to the morning of January 1st, not the whole day. The character 旦 depicts the sun rising above the horizon, representing dawn. However, in modern usage, many people use 元旦 to refer to all of January 1st.
Common collocations
Related words
元日 refers to the entire day of January 1st. 正月 refers to the broader New Year period (typically the first few days of January). On New Year's cards, 元旦 is commonly printed as a closing mark, meaning "delivered on New Year's morning."