Is there a generic word for "thread or process"?
A process is a context with one or more threads of execution (concurrent with other threads of execution, either in the same process, or perhaps in other processes), and with its own address space (and usually other resources such as open file descriptors, IPC mechanisms, etc.).  More subtle details and implications are described here

So, if address space (and other such resources) isn't relevant to your discussion (and it's probably not given your description), then I would say that the word thread is sufficient to describe the entities involved in your discussion.  Historically task has also been used to describe a thread, and indeed it was perhaps the first word used to describe this concept (see this).

(Note of course there's a difference between concurrent threads and parallel threads -- concurrent threads may be executed in parallel, but it is not necessary for operations to occur in parallel for them to suffer from the issues related to concurrency.)