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The phrase "differences arose between" is correct and usable in written English.
It is usually used to describe disagreements or conflicts between two parties. For example, "Differences arose between the two groups when they disagreed on the best way to address the problem."
Exact(18)
When differences arose between people of different colors, those of one color would say: "We have worked for many years to create a land of equality for all our citizens and we have come a long way.
Much bigger differences arose between the employment of blacks and whites.
Differences arose between the employees who were on strike and the company and those employees who continued to work.
In 1968 serious differences arose between Mr. Sippy and the director Bhappie Soni during production of "Brahmachari," starring Shammi Kapoor, and the project was nearly shelved.
Differences arose between loblolly and shortleaf pine in both the contribution from each state inventory pool and the number of points used in the final model fitting.
Irreconcilable differences arose between the band members and they went their separate ways in 2009 – with a brief reunion at Coachella 2013 – until this year, when lead singer Gordon Gano announced that Violent Femmes had reunited.
Similar(42)
Specifically, potential differences arise between firms paying dividends with tax credits, paying dividends without tax credits, and not paying dividends.
Differences arising between the parties under the Armistice Agreement should always, in our opinion, be handled as fully as possible in the first instance by the Mixed Armistice machinery.
The costs of those kinds of patterns may be minimal in certain contexts, but in others the fact that differences arise between us may cause a loss of our fundamental democratic institution.
The products have been characterised by size exclusion chromatography and 1H NMR and FT-IR spectroscopies and interestingly though the trends in copolymer structure are similar for products prepared in the conventional glassware and those in the parallel reactor, some systematic differences arise between the two sets of products.
But unlike its application to households and firms, when austerity is applied to government, wide interpretative differences arise between Keynesians and Saysians, because they embody wholly opposite principles and policy prescriptions.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com