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The phrase "a second difference between the two" is correct and usable in written English.
It can be used when comparing two items or concepts and highlighting an additional distinction between them.
Example: "In addition to the first difference, there is a second difference between the two that is worth noting."
Alternatives: "another distinction between the two" or "a further difference between the two".
Exact(3)
A second difference between the two companies is their profitability.
A second difference between the two curricula lies in the role that definitions play.
A second difference between the two proposals is that the phase plots of p t) vs. n k (t) (see Fig. 11) will be straight for cells obeying Eq. 15, but they will be systematically curved for cells that are ruled by Eq. 16 (not shown).
Similar(56)
The third difference between the two research groups is related to their learning abilities.
There is a second crucial difference between the two scenes.
Second, the difference between the two trains of repetitive stimulation was significantly different for trigeminal stimulation.
There is a difference between the two.
First, the differences between the two examinations were calculated for each patient.
A first evident result was the large difference between the two principal residual stress components.
And the third saw "no essential difference" between the two.
The first and most important difference between the two is the arteriovenous oxygen difference.
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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