As mentioned by @marc_s, @Cloud, et al. they're basically the same for a closed range.
But any fractional time values may cause issues with a closed range (greater-or-equal and less-or-equal) as opposed to a half-open range (greater-or-equal and less-than) with an end value after the last possible instant.
So to avoid that the query should be rewritten as:
SELECT EventId, EventName
FROM EventMaster
WHERE (EventDate >= '2009-10-15' AND
EventDate < '2009-10-19') /* <<<== 19th, not 18th */
Since BETWEEN
doesn't work for half-open intervals I always take a hard look at any date/time query that uses it, since its probably an error.