A recreational pilot certificate only allows flights within 50 miles of home airport. A sport certificate has no distance limits even though it's easier to get - no medical certificate, less flying time and less instruction. What's the reason?
The Recreational Pilot PTS and Sport Pilot PTS look nearly identical, but the key to your question can be found under AREAS OF OPERATION, Section I. PREFLIGHT PREPARATION. Sport Pilots are required to demonstrate "Cross-Country Flight Planning", whereas Recreational Pilots are not.
Since they are not required to demonstrate the ability to plan a cross-country flight, unlike Sport or Private pilots, Recreational pilots are not allowed to perform them without an additional endorsement.
Because a sport pilot certificate requires the applicant to undergo at least three hours of cross country flight training whereas a recreational pilot certificate does not have that requirement.
I always got the impression that a recreational pilot certificate was essentially for people who had soloed and did not want to accomplish any other aviation goals save flying around their local airport. Instruction is restricted to pre-solo aeronautical knowledge and skills. It’s pretty limited in capability compared with a private pilot certificate, which explains why there are less than 600 recreational pilots registered by the FAA.
And one can expand a recreational pilot certificate to permit PIC on cross country flights over 50 nm, but this will require additional training and logbook endorsements by an instructor
To put it short, the Recreational Pilot certificate allows you to fly common aircraft such as the Cessna 152. The Sport Pilot certificate was only created recently (2004), and it restricts the owner to Light Sports Aircraft - 1300 lbs MTOW or less.
Pilots on a budget normally get a well-used plane, and that's rarely an option for LSA, just because they're all quite new. Right now a well-used light aircraft can still be bought cheaper than a new LSA. So the Recreational path still has a lower financial entry barrier.
Long-term, the Sport cert appears to be meant to displace the Recreational. LSA restrictions are more practical and reasonable, given modern-day technology. Anyone who can't find a LSA that's good enough for them isn't likely to be satisfied with Recreational Pilot restrictions either, and will go for the proper PPL.
Because the spirit of the regulations are a bit different and there is some history tied to this. The recreational pilot cert allows you to fly a lot of lighter common GA planes (J-3 Cub etc.) but limits you to one passenger and a local area. The idea being that the training is reduced a bit but you dont really need to worry about complex navigation, long range weather planning or any of the stuff that comes with flying a capable plane, far. The cert was intended mostly for local weekend fun in aircraft that were already easily rented.
The sport pilot cert was intended to birth a whole slew of aircraft but the type never really took off. Since new limitations were in place the hope was makers would build new planes but the reality was that a new sport plane cost well more than a nice used GA plane. You could often take the difference and get a full PPL as well as an instrument rating and still have some left over. Sport planes are fairly useable in some regards and pretty docile so the training was matched to the intended plane more than to complete with recreational.