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Google ngrams supports those sources that say "Patagonian Missionary Society" rather than "Patagonian Mission". More research needed. All the best: Rich Farmbrough 13:21, 11 June 2024 (UTC). reply

Checking Google Books supports the longer title to refer to the society itself, certainly on more formal documents such as books (compared with letters transcribed verbatim). All the best: Rich Farmbrough 13:48, 11 June 2024 (UTC). reply