My understanding is that the 924 was designed by Porsche to be built by Audi and Volkswagen as a joint effort. Then VW backed out and Porsche assumed its role. The 924 was built in an Audi plant with an Audi engine. The 944 had a Porsche engine, but was still assembled by Audi. Porsche then took over the project, redesigned the car 80%, and built the 968 at their own factory. Wikipedia, which of course could be wrong, states as follows:
"Porsche's 944 model debuted for the 1982 model year, was updated as "944S" in 1987 and as "944S2" in 1989. Shortly after the start of production of the S2 variant, Porsche engineers began working on another set of significant upgrades for the model, as executives were planning a final "S3" variant of the 944. During the development phase, 80% of the 944's mechanical components were either significantly modified or completely replaced by the engineers, leaving so little of the outgoing S2 behind that Porsche management chose to introduce the variant as a new model, calling it the 968. In addition to the numerous mechanical upgrades, the new model also received significantly evolved styling both inside and out, with a more modern, streamlined look and more standard luxury than on the 944. Production was moved from the Audi plant in Neckarsulm (where the 924 and 944 had been manufactured under contract to Porsche), to Porsche's own factory in Zuffenhausen."