How is statistical equivalence testing different from post hoc tests done after ANOVA?
The post hoc tests following an ANOVA are pairwise t tests for mean difference. They have null hypotheses that the population means are equal (alternatively that the difference in population means is zero). Also, there are some post hoc details like pooled variance and multiple comparisons adjustments. We can set those aside, as they are largely irrelevant to your question.
By contrast, tests for equivalence (which could be, but are not necessarily post hoc tests following an ANOVA), have null hypotheses that the population means are different by at least some researcher-defined amount. You might get something out of reading the tost tag description.
One can combine the inferences from difference and equivalence tests, as I point out in my question here.