Ngram Viewer for tureen and terrine broken down
From what I could find
tureen is the Anglicised version of
terrineFor GB English and US English,
tureen is fairly equal during the entire period.
For GB English and US English,
terrine is negligible until mid-1970s when it began climbing rapidly for both (I'm sure there is a reason for that! — some cookbooks on French cooking which wasn't satisfied with the existing, Anglicised version of the word?). But starting in the late 1990s,
terrine appears continue its rise in frequency for GB English but NOT for US English where its frequency flattened. Then, about 2010,
terrine's appearance in GB English skyrocketed whilst dropping in US English.
By 2019,
terrine is used more than four times as frequently in GB English (0.0000332931%) as US English (0.0000082637%).
The OED doesn't distinguish types of English for its typical frequency calculations, but shows
tureen 'typically occurs about 0.2 times per million words in modern written English, whereas
terrine 'typically occurs about 0.1 times per million words in modern written English'. IMNSHO, a word used only half as frequently as tureen probably isn´t 'common'.