Before we get into the details of the answer to this question, my recommendation is – If you’re looking to purchase a copy of FSX, the only version you should consider is Flight Simulator X – Gold Edition. At a typical price of $28 US or less on Amazon.com, it is really absolutely the best choice. It contains both FSX Deluxe AND the FSX Acceleration expansion pack, which itself updates FSX to the latest version (Service Pack 2 (SP2)), and adds many other additional features, including new aircraft and new functionality, such as the ability to race your friends online land on aircraft carriers.
So, what’s the difference between the Standard and Deluxe editions of FSX? From the Wikipedia article for FSX:
Flight Simulator X was released in three editions: Standard, Deluxe, and later Gold. The Deluxe Edition incorporates additional features, including an on-disc software development kit (SDK), three airplanes with Garmin G1000 “all glass” avionics, and the ability for the player to act as Air Traffic Control (ATC) for other online users with a radar screen.
The Deluxe Edition features 24 aircraft compared to 18 in the Standard Edition; 45 high-detail airports compared to 40; 38 high-detail cities compared to 28; and 51 structured missions compared to more than 30.
In particular, FSX Deluxe adds the Garmin G1000 avionics to the Cessna 172, Beechcraft Baron 58 twin, and to the Mooney M20M Bravo. It also adds the Grumman Goose floatplane, and the ability to fly the Maule Orion bush plane. The Acceleration addon also adds the P-51D Mustang Racer (with the ability to recognize damage if you overrev the engine), the Agusta Westland AW101 rescue helicopter, and the Boeing F/A-18 Hornet Navy jet fighter.
Check out the Wikipedia article for even more detailed information on the differences between the two versions and what the Acceleration addon pack adds.