In Series or in Sequence?

In Physics, we talk about having circuit elements in "parallel" (current splits to go through either but not both) or in "series" (same current goes through one element and then the next).

In plain english though, we do the steps of a project in parallel (at the same time) or in sequence (one after the other).

So what is the difference between series and sequence? 

In Math it is the difference between an ordered set (sequence) and the sum of that ordered set (series). 

For everyday usage, dictionary.com supplies the following:
"Series is applied to a number of things of the same kind, usually related to each other, arranged or happening in order: a series of baseball games. Sequence stresses the continuity in time, thought, cause and effect, etc.: The scenes came in a definite sequence."

The Latin roots of the words are "connection" (series) and "to follow" (sequence).

It seems to me that the best alternate to "parallel" (from the greek "side by side") in the physics sense is actually "sequence" not "series".  In both series and parallel circuits, the resistors are similar and arranged relative to each other as well as being connected so there is almost not enough distinction between "parallel" and "series"!

So why do we say "series circuit" instead of "sequence circuit"?  It turns out that the total resistance of a bunch of resistors in series is the sum of all the individual resistors - so it looks like a mathematical series (being added).

I wish the parallel circuits had a formula for total resistance that reminded one of geometric parallel-ness, but (as far as I know) they do not.  So there is no good parallel for a parallel circuit, be it series or sequence...