Date of conception is wrong

Hi, I am very confused on my pregnancy. Yesterday, I was told I am 8 weeks pregnant with 3 days. The doctor said my date of conception was around October 3-7 or so but when I went to confirm the pregnancy the first time, different location, the doctor said my date of conception was anywhere between September 19-24. September is when I had intercourse so I am so confused because it was around the 20th or so but this other doctor said that impossible and there is no way. Has this happened to anyone else? He also used a very old ultrasound machine, could that be a reason why it might be off?