The Spurs extended Leonard a qualifying offer mostly as a formality, as they were going to offer him a five-year max contract as soon as he became a free agent. For Aron Baynes and Cory Joseph, receiving a qualifying offer was the difference between restricted and unrestricted free agency and only the Canadian point guard got one.
For the Spurs to have the cap room available to sign LaMarcus Aldridge both Joseph and Baynes will likely have to be renounced, so neither was expected to return. This decision doesn't affect that significantly but it does make it harder to imagine a scenario in which Baynes suits up for San Antonio next season.
Last summer NBA teams stayed away from Baynes because he was a restricted free agent. After the market dried out, he re-signed with the Spurs instead of going to Europe for similar money. Now he's free to negotiate with whomever he wants, which means he might sign elsewhere while the Spurs are busy trying to lure LaMarcus Aldridge to San Antonio. The Spurs might have been afraid that he was going to sign the QO and that's why they didn't tender one or Baynes might have asked for them not to, to pursue other alternatives.
Joseph, meanwhile, will become a restricted free agent, which means the Spurs will be able to match any offer sheet he signs. It doesn't mean he will be retained but since his qualifying offer is $500,000 lower than Patty Mills' contract, there's a chance that if the Spurs need to clear a small amount, they trade Mills and keep Joseph. There's likely a verbal agreement in place with Joseph to not accept the qualifying offer and the Spurs can always elect to renounce him if signs an offer sheet.
Of course, this is all speculation at this point but it's interesting nonetheless that the Spurs handled their two potential restricted free agents differently.