This happens all the time. If the label is created late on a Friday say or just before a holiday, the shipping department will show it as shipped even though the carrier hasn't picked it up. This happens at Bud's and everywhere else.
There are, at times, other issues I have seen at placers other than Bud's where shipping departments carrying an order as processing even though it has shipped. I've even received shipments still awaiting processing (from others, not Bud's). Still in doubt, call Bud's.

I had a pistol listed as not yet shipped and my FFL called me and said she received it. It all depends when and how their updates are processed.

This happens quite frequently as the item is marked as "shipped" by Fedex, USPS, or UPS but in reality it could mean the shipping label has just been created. When it starts moving along and gets scanned is when you'll see the actual shipping.

This has happened to me not only at Buds but almost everywhere else I shop on line. Basically, your credit card or bank account has been charged, the paperwork has been completed, the item has been boxed, a shipping label created (the shipper is also automatically notified an item is ready for pickup) and the item is at the "loading dock" waiting for the shipper to pick it up. As far as the merchant is concerned (in your case Buds), it has shipped. When the shipper picks up the item, they scan the label but it often takes a few hours to a day (don't know why) to show up as picked up. That's more or less how it works with just about any on line merchant, even Amazon and they're probably the most mechanized and responsive on-line retailer in the business.

It was a holiday weekend so Buds might be playing catch up today. Things should be back on track today

They don't always match up verbatim. You might just keep an eye on it. It should change with fedex in a day or so. If not, you may just send an inquiry to FedEx to see if they have obtained the package and started shipping it.