words - When would you use 相互 as opposed to お互い？

I'm thinking the former is slightly more hard/archaic, and for written style japanese, where was the latter is more conversational? But they both seem to have the same meaning.

Answer

I'm thinking the former is slightly more hard/archaic, and for written style japanese, where was the latter is more conversational? But they both seem to have the same meaning.

• 相互 is slightly more hard: yes.


• 相互 is slightly more archaic: no.


• 相互 is for written style: yes


• お互い is more conversational: yes.


• they both seem to have the same meaning: yes.

Jisho.org defines them as:

相互{そうご}
Noun, No-adjective
1. mutual; reciprocal

お互{たが}い
Noun
1. mutual; reciprocal; each other
Polite form of 互{たが}い

互{たが}い
Noun

1. mutual; reciprocal​

According to the above definitions, 相互 and お互い/互い seem to have the same meaning and be interchangeable except for 相互 having No-adjective as a part of speech and except for お互い being polite.

However, their actual use or nuance is slightly different, and they are not always interchangeable.

As for お互いに/互いに and 相互に which are the adverbial forms of お互い/互い and 相互 respectively, they have the same meaning as "mutually; with each other; reciprocally; together", and are almost interchangeable.

But, as for お互｛たが｝い様{さま} which is often used in a conversation or in salutation meaning "we are of equal status in this regard", お相互｛そうご｝様{さま} or 相互｛そうご｝様｛さま｝ doesn't make sense at all.

I think the biggest difference between 相互 and お互い/互い is that the former can make compound words as follows, while the latter cannot.

• 相互作用{そうごさよう} interaction


• 相互理解{そうごりかい} mutual understanding



• 相互交流{そうごこうりゅう} mutual exchange


• 相互運用性{そうごうんようせい} interoperability


• 相互扶助{そうごふじょ} mutual aid


• 相互協力{そうごきょうりょく｝bilateral cooperation

The difference in the nature of both largely comes mainly from the word where they were born. お互い/互い are Yamato kotoba (大和言葉) or Wago (和語), which are native Japanese words, while 相互 is Kango (漢語) or Sino-Japanese vocabulary, which refers to that portion of the Japanese vocabulary that originated in Chinese or has been created from elements borrowed from Chinese.

The major difference between Wago and Kango reflected in お互い/互い and 相互, in general, is that the former has a comprehensive meaning, is not official, is suitable for colloquial use and has emotional nuance, whereas the latter has a relatively strict meaning, is suitable for official usage and written language, and has a descriptive nuance.

A related article: What are the differences between わけ and 理由?