There seems to be a lot of confusion about the Air's Storage.
The Macbook Air comes with an SSD which uses an custom mini-PCIe/mSATA connector also found in some Dell and ASUS computers.
Some notebooks (notably the Asus Eee PC, the MacBook Air, and the Dell mini9 and mini10) use a variant of the PCI Express Mini Card as an SSD.
The connector on the motherboard looks like this (the one on the left):
The SSD looks like this:
The Macbook Air does not drop the SATA interface. It uses a variant of the mini-PCIe/mSATA connector. You can buy upgrades which work at up to 6GBPS here for example.
Apple uses the term Flash Storage as it's exactly what this Solid State Drive is as opposed to the mechanical counterparts Hard Drive Disks. An SSD is (mainly) composed of a main board, a connector, a controller and flash memory chips. At least modern SSDs use flash memory as opposed to RAM based SSDs (with backup batteries for storage or without for temporary operations).
The great advantage of the smaller SSD with mSATA connectors comes from their form factor. They are slimmer, thiner and take less room on the motherboard. Smaller connectors require less space and less circuitry to connect with other components.
When you look in the system info the drive shows up as a standard SATA SSD.
If you want to connect the SSD in a laptop or desktop PC there are some pretty siple adaptors like this one:
It seems out of scope but for a good overview of the advantages of SSDs and HDDs see here.
Note: I previously thought the connector was a stock mSATA connector which is a PCI Express Mini Card-like connector which is electrically SATA. But apparently it is a variant. See this question for more info about the connector.
My wife owns one of these and they are great at retrieving large amounts of data and launching programs with large libraries (iPhoto, iMovie, iTunes...).
But a Macbook with a similar standard 2.5" SSD will be just as fast.