They tell you when you conceived, but ON or AROUND that day...not that exact day. No one can tell you the exact day you conceived. Sperm can live inside your body up to 5 days, so if you had sex with a guy July 31 and Aug 4, the guy from July's sperm may have still been inside you and the Aug guy's sperm could have been in there too (since you don't know if you used a condom) SO either guy could be the father, sorry to say...but you definitely need a paternity test to know who the father is. There's no way to tell other than the test.
the only way you're going to know is a paternity test.
Well you don't necessarily conceive the day you had sex. You may have ovulated the day after or so and that is when conception happened. The dates are so close together it is hard to tell when you really conceived but from the dates they are giving you it sounds like it is the 1st guy....but dates can be wrong. Hope everything works out well for you.