I think the main difference is that the CDC 6600 the PP state barrel would rotate in a regular way constantly multiplexing the execution of the 10 virtual PPs in the same hardware.
Hyper threading is the idea where the multiplexing of multiple threads happens dynamically based on data dependencies / stalls.
Fundamentally they are the same SMT concept though: multiple hardware threads that have separate register (and other) state but share an execution unit.
HT as an implementation tries to give long sequential execution windows to a hardware thread, it's designed to hide occasional long latencies (IO typically), but pays by having a higher switching cost.
A barrel processor trades off individual instruction latency for a higher degree of parallelism and improved latency hiding.
Hyper threading is the idea where the multiplexing of multiple threads happens dynamically based on data dependencies / stalls.