number of weeks pregnant or the age of the fetus?

Hi, I live in Belgium and I'm a bit confused. First, my GP said I was due on March 17, but after the ultrasound with the gynecologist, it turned out to be April 12. The "8 weeks and 1 day" mentioned on the report refers to either the pregnancy week or how old the baby is. The books I have say these are two different things, which is really confusing because I keep thinking, "Oh, now we're there," but nothing adds up. Can someone try to explain this to me? We're going back for an ultrasound at the end of the month, and I'll ask for clarification then. I feel quite silly at the moment. Greetings.