I think you're correct that in a general sense 8.1 includes 8.5.1. But 8.1 is much broader in scope. It covers planning for all of operations, including customer requirements, design, purchasing, etc. 8.5.1 only includes the production (and service) operations.
You could probably say there is a similar relationship between clauses 4.4 and 8.1. 4.4 covers planning for the entire QMS including leadership, resources, operations, supporting processes, etc. while 8.1 only covers the operational aspects of the system.