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Peripheral:

Something that is peripheral is not as important as something else: The book contains a great deal of peripheral detail.

Incidental:

Less important than the thing something is connected with or part of: Try not to be distracted by incidental details.

To me, based on dictionaries, these two words are so close that I hardly can differentiate them from one another.

For instance, I cannot tell the following collocations apart:

  • peripheral / incidental problem
  • peripheral / incidental information
  • peripheral / incidental role
  • peripheral / incidental activities

Also, Ngram proves that there are lots of hits for all these combinations including both of the adjectives in my question.

Does it mean that these two words are the same? If not, how do they differ?

Which choice is better with each words: "problem", "activities", "information", "role", "issue" etc?

How shall I diagnose the proper combination?

Please let me know about it.

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Neither "peripheral" nor "incidental" really means 'not important or "not as important as something else".

Peripheral

The word "peripheral" means "not central", coming from "periphery" -- the border or edge of a geometric figure, especially a circle. Something that is peripheral in one context may well be central in a different context.

The book on Asian languages contained a lot of peripheral discussion about Japanese culture.

That information, peripheral to a study of language, might be utterly central to a study of culture. However, peripheral information is often less important to a reader or student than is central information -- when studying that topic. Therefor designating something as peripheral often means that it is not as important -- for the specified purpose.

Incidental

The word "incidental" means "encountered by the way", or "noticed while doing something else". Sometimes something that is incidental turns out to be of much greater importance than the intended project or activity.

The discovery of penicillin was incidental to a study of the growth of bacteria.

Many serendipitous discoveries start with something that was incidental to the task at hand.

Comparison of the Two

All that said, when something is not at the focus of the task at hand, it is often both "peripheral" and "incidental" to that task. In such cases either word can be used, and in practice there will be no significant difference in meaning.

  • Thank you very much @David Siegel. Hence, for all my offered constructions in my original post and in the meaning "not central" and what comes "in margines", can I use both adjectives and have identical connotation? Also for some other words like: "expences" and "discussion". Please tell me more about it. – A-friend Jun 6 at 5:34
  • I don't know why, but "incidental" has a connotation of both "peripheral" and "additional/extra" at the same time for me @David Siegel. Mayebe because it has the meaning of anything that you face unexpectedly or rather you bump into. Do you think like me? Is it the same for you David? – A-friend Jun 6 at 6:08

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