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'the difference occurs' is correct and usable in written English.
You can use this phrase when you want to explain that something is different or to refer to a difference. For example: "The difference occurs when the two ingredients are mixed together."
Dictionary
the difference occurs
noun
The quality of being different.
Exact(6)
The difference occurs in the positive image, which may be composited from either the additive or subtractive primaries.
Twenty-five genes on the X chromosome and one gene, CASP6, on Chromosome 4 were identified a significantly sex difference and the difference occurs in both directions.
The difference occurs because disease can only be observed if the invasive, yet sensitive and specific secondary test is used.
In the European model (including Australia) HEMS are staffed by well trained physician/paramedic/nurse teams and this is possibly where the difference occurs for survival for TCA patients.
More research with larger sample size is needed to understand whether there is gender difference in the association between childhood parental divorce and mental health outcome and why the difference occurs.
For example, for a 30 bp read to map to a reference with only one difference, there must be at least 15 consecutive bases, called a seed, that match exactly regardless of where the difference occurs.
Similar(54)
The difference occurred due to different logistics in the permanent facility where FFDM was installed, whereas most SFM units were functional in mobile facilities.
The difference occurred, Mr. McCall said, because the administration did not fully account for fines and other money that would have been collected.
The difference occurred in spite of similar aboveground productivities and root biomass.
A statistically significant difference was the likelihood of the difference occurring by chance of less than five percent (P < 0.05).
We believe that this result is due to the difference occurring in the layouts of the two buildings and within each level of the buildings.
More suggestions(15)
the difference comprises
the difference affects
the difference producing
the difference attributable
the difference revolves
the difference product
the difference procedure
the difference originates
the difference corresponds
the difference contributes
the hiring occurs
the scene occurs
the disorder occurs
the difference is
the disconnect occurs
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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