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Notes -
The null hypothesis is indeed one of a set of competing hypotheses, but it’s typically the one that assumes no difference between populations.
If I want to show that two distributions are statistically different then I start with the assumption that they are not and then set out to disprove that.
Similarly, if I believe the populations are not actually significantly different, I believe it’d still be common to set up a null hypothesis that they are not different and then either confirm or reject the alternative hypothesis.
And what assumption do you use when you want to show that they are the same? It's just a matter of how you formulate your question.
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