Learn English – An alternate word for a feeling of unbelonging

I think the difference is in degree. It's similar to the difference between large/huge/gigantic or small/tiny/miniscule. In some contexts, you may be able to substitute any of those words, but due to common usage or word origin or whatever other factors, there is an understood subtle scale.

So, if you have relevant facts to discuss, they may or not be important, but they are related to the matter at hand. But if you have pertinent facts to discuss, they have precise or logical relevance to the discussion. They absolutely should not be overlooked. Pertinent facts are always relevant, but relevant facts are not necessarily pertinent.

One reason why this may be the case is that pertinent could also be used as a synonym for apt (ie. strikingly appropriate) but relevant doesn't really have that meaning. If I said you wrote an "apt answer" to this question how would you feel? What if I said it was a "pertinent answer?" Or "relevant answer?"

I think most people would feel that calling it a relevant answer is nearly a mild insult. Oh yeah, it's related, but not close to perfect.

Like J.R., I don't see a good match between the language of the quoted sentence and any clear, recognized definition of churning.

The only definition of "churning away" that I'm familiar with carries a sense of purposeless activity; essentially it means "churning without a definite goal or foreseeable end," as in "He left the refrigerator door open, and the motor was just churning away all afternoon."

"Churning away" emphatically does not mean churning productively—not even at the impersonal, quota-driven level of "churning out," which, as Merriam-Webster's Eleventh Collegiate notes, involves "produc[ing] mechanically or copiously," but which frequently harbors an implication of poor or indifferent quality in the resulting output.

Making sense of the author's description of women churning away "dreams, fears, social [intrigues] and political intrigues" is complicated by the fact that one of the churned-away things (dreams) seems desirable, a second (fears) seems undesirable, and a third (intrigues) may be desirable or undesirable. Under the circumstances, it's hard to tell whether the women intend the churning to produce these things—or indeed whether the women have any clear intention at all with regard to their churning.

Maybe the author chose "churning away" to avoid the unflattering implications of "churning out." If so, I think it was a bad decision, since "churning away" does an exceedingly poor job of conveying what (I suspect) the author means. I would have suggested ending the sentence as follows:

...where the women of the home give voice to dreams and fears, and where elaborate social and political intrigues play out."

An author determined to tie the sentence to a kitchen-friendly verb could have used "cook up" or "brew up." Both have weaknesses of their own—"cook up" suggests fabrication of a deceptive kind, and "brew up" has witchy connotations—but at least they aren't borderline nonsensical, as "churn away" is.