I have worked with state funded shelters and privately run rescues. They seem to be the same on the outside, but they are vastly different.
First off, shelters are usually state funded, so they are able to do the same services as rescues but charge the adopter a lot less. Rescues are funded solely on adoption fees as well as private donations. But on the flip side, the dogs in a shelter are kept in a shelter environment. The dogs receive almost no extra socializing, training, etc. In a rescue, dogs are usually kept in a foster home, where they are further evaluated, trained, socialized, etc.
Basically in a shelter, the dogs are adopted out in the same condition they were surrendered in. It is hard to fully evaluate a dog in a shelter so you may get what you've been promised, you may not, whereas a rescue has the dogs in a home setting where its behavior can be monitored and watched to the extent that they are able to tell you exactly what you are getting. They usually come to you better adjusted, better evaluated, better socialized so to speak. Not to bag on shelters because they have wonderful dogs and do a wonderful service, but rescues are able to take it one step further and do what shelters cannot. But because rescues do not recieve state funding, they do have to charge more.