I was brought up with one of my father's pet peeves of using 'between' for two and 'among' for three or more. Usage has changed, however -- see escoville #3. I would expect to to see "between" in this context of intergroup comparisons these days.
intergroup comparisons - between group
intragroup comparisons - within group
=> "There was no difference between the three groups with regard to the XY concentration".
But that may also reflect my British viewpoint and with the proviso that IAN a statistician.
Just out of interest:
BMJ search results (as phrase) in full text , from Jan 2015 to Jun 2021:
86 for 'difference between groups'
79 for 'differences between groups'
0 for 'difference among groups'
2 for 'differences among groups'
JAMA (same period, Jan 2015 to Jun 2021)
1336 results for "differences between groups"
69 results for "differences among groups"