Fun Bonus Fact: We drove to DC, so we could have just driven there, but thought a cheap Bus round trip was more fun as we could both see the sights, and not stress about traffic.
You visited the udvar-hazy center which is out by Dulles airport in Chantilly. It is still part of the smithsonian, but more focused on displaying lots of different aircraft in a few large hangers. Very impressive and worth a visit, but not the main air and space facility.
Either you had a legitimate miscommunication, or you got scammed by your driver. No one from around the DC metro would confuse the two.
Although I did my paranoid pre-trip research [partial thanks to dad], I can understand the confusion.
That said, I've been to the Air and Space museum a handful of times, and I only go back when I have visitors in town who want to do the tourist thing.
The udvar-hazy faculty is something I'll visit on my own over and over again. It's an incredible collection of important machines including the discovery space shuttle, an SR71 blackbird, the Enola Gay, etc.
The museum at Dulles features a lot of much larger aircraft and a lot of the more niche technical displays that they can't justify the space for in DC.