Electric engineering talks about parallel and series. (including the old parallel and serial ports on computers, before almost everything became serial)

Programming talks about parallelism or concurrency or threading. (single-threading, multi-threading)

Or synchronous and asynchronous.

The legal system talks about concurrent and consecutive.

Process descriptions might use "sequential" rather than consecutive or series.

"Linear" is another possibility, but it's overloaded since it's often used in reference to mathematics.

Both would be understood and are roughly interchangeable.

"Sequential" feels more appropriate to me for the task runner scenario where we wait for one task to finish before running the next.

"Series" suggests a kind of concurrency to me because of the electrical circuit context, where the outputs of one are flowing into the next, but both are running concurrently. Processes that are Unix piped into each other would be another thing that feels more like a "series" than a "sequence".

The electronics terms parallel and series are about static physical connections (things are connected in parallel or series — the more grammatical form would be in a series).

The software terms parallel and sequential are about the temporal relationship of activities (things are done in parallel or sequentially). That’s why in software we also have the term “concurrent” which means something different from “parallel”.

When talking in terms of software parallelism, "parallel" and "sequential" are more common to describe, for example, multi-threaded vs. single-threaded implementations.

Sequential is a fuzzier word. It can imply that a series of steps feeds output from step A into step B and so on. But at the same time it can also drift into areas typically defined as linearization. Where a task runs in parallel but applies in series, in sequence.

I think your average person knows what sequential means but might not remember what series means. Personally I always remember the meaning of series in “parallel vs series” because it must be the opposite of parallel. I’m not proud of the fact that I always forget and have to re-intuit the meaning every time, but the only time I ever see “series” is when people are talking about a TV show or electronics.

Parallel and Series makes sense to me; it's also the terminology used for electrical circuits.