Determinism is making sure the digging is in the right place. Non-deterministic digging may be possible, but it's harder to get right.
Concurrency could also be having one guy with one shovel, but digging iteratively in 5 separate places and digging a shovelful or two at a time.
Or to put it another way, parallelism is digging two ditches with 4 people 4 times as fast as 1 person digging two ditches; concurrency is 1 person digging two ditches at the same time, alternating; determinism is making sure that the two ditches are being dug correctly, at an even pace, etc.
Concurrency could also be having one guy with one shovel, but digging iteratively in 5 separate places and digging a shovelful or two at a time.
Or to put it another way, parallelism is digging two ditches with 4 people 4 times as fast as 1 person digging two ditches; concurrency is 1 person digging two ditches at the same time, alternating; determinism is making sure that the two ditches are being dug correctly, at an even pace, etc.