This sounds like the Access is interpreting your date as dd/mm in the first case and mm/dd in the second.
Try using format yyyy-mm-dd which should always be interpreted correctly. In other words
Select BMID,UserId,Format([PDate],'dd-MM-yyyy') as PDate1,PName
From BodyMeasurements
where UserId=1
And BodyMeasurements.[PDate] between #3015-07-19 12:00:00 AM# and #2015-08-18 11:59:59 PM#