18th day of the month
Refers specifically to the 18th day of a month, not a duration.
The meeting will be held on the 18th.
18 days
Indicates a period of 18 days. Often used with counters or in contexts like 'for 18 days'.
This work took 18 days.
Explicitly means 'a period of 18 days', while １８日 can mean either the date or the duration depending on context.
Standard Arabic numeral spelling; very common in calendars and schedules.
Kanji spelling; equally common, especially in formal or vertical writing.
Mixed kanji-numeral spelling; occasionally seen but less standard.
Compound of 十八 (じゅうはち, 'eighteen') and 日 (にち, 'day'). The reading にち is the standard on-yomi for 日 in date expressions.