sequences and series

I think that learning math has colored my ideas about the connotations of words. In particular, the words “sequence” and “series” have the meanings “a set of related things that follow each other in a particular order” and “a number of things of a similar nature coming one after the other.” They appear to be mostly interchangeable. But consider the phrase “in a sequence/series of of papers, Csiszár and Narayan proved…” Is there a difference in meaning?

To me, “series” connotes a cumulative effect — the set of papers build upon each other, as in the summation of a series encountered in calculus. The word “sequence” is milder — these are set of related papers that follow chronologically, but may look at different angles of the same problem rather than building on each other. Clearly this difference is leaking in from the technical definitions into my writing. Does this happen to anyone else?