Those aren’t contradictory. Centralized planning refers to organizing aspects of the economy, in particular things with inelastic demand, through the government (the public sector). It’s run as a business, same as in the private sector, except profit is not the point. It can be organized based on a capitalist mode or a socialist mode. If it’s organized in a socialist mode, the entire body of workers have a say in the process of the central planning.

Centralized planning is critical for inelastic demand, such as housing, healthcare, and for the most part food. It is not a replacement of markets, it is supplementing them to ensure basic necessities are available to everyone. The private market can still exist just fine, it’s the organization within the companies that change. The ratio of public to private, and planned economy to market economy, depends on a significant amount of factors, internal and external.