I select Find Issues,
I have a date field and I enter a date in the "(after)" field.
JIRA includes records with the entered date as opposed to records greater than that date.

Example:

Date Field: "Planned Implementation Date"
Find Issues - Select all records with Planned Implementation Date (after) December 1, 2005

I expect to find records with Planned Implementation Date from December 2, 2005 and greater. However I get records with Planned Implementation Date = December 1, 2005 and greater.