The Street Edition was just another marketing attempt 'special' package - GM was always doing this sort of thing with colours or other options not available for the normal cars, so that people would view them as being collectible and buy them. It often failed to work - they'd set a 500 (or whatever) limit on the edition and it usually failed to sell out, making the cars rarer than they had planned, which probably suited the people that bought them just fine.
I have a copy of the Street Edition brochure and the following is copied and pasted from that. The differences between that and a stock NA were (and remember that this comes from a brochure and that GM didn't always follow up with what they said in practice on every single car):
Unique Features
• Black heritage stripe on hood and decklid
• Black headlamp bezels
• Black GXP style front grilles
• Z0K racing-inspired suspension
Includes Solstice standard
equipment plus:
• Brazen Orange Metallic exterior color
• Ebony leather seating surfaces
• Sport pedals
• 6-disc in-dash AM/FM/CD changer
• 7-speaker premium sound system
• Air conditioning
• Carpeted floor mats
• Preferred Package
• Convenience Package
• Premium Package
Pricing
With manual transmission: $29,310*
With automatic transmission: $30,305*
Optional rear spoiler: $275 MSRP
Basically an NA but with GXP trim and suspension (NA ZOK = GXP standard) and some rather nice wheels, which I use on my coupe because I think they were the best looking stock wheels of the ones offered and early exposure to the coupe publicity photos showing them left me unsatisfied when I couldn't buy them on a coupe!