13th day of the month
Used to specify the 13th day of any month. Often appears in dates like １３日（じゅうさんにち）.
The meeting will be held on the 13th.
13 days
Used to express a duration of 13 days. Often followed by a counter or in phrases like １３日間.
This work took 13 days.
The meeting will be held on May 13th.
I couldn't go outside for 13 days after being hospitalized.