While most sources state the difference between one-way anova and one-way repeated measures anova as
The same subject undergoes different and all levels of the within-subject factor in one-way repeated measures anova, while each subject in one-way anova has only 1 measurement.
In the anova table of one-way repeated measures anova, subject SS is decomposed and separated out of SSerror when forming the F-Statistic.
It is commonly stated that the model equation of one-way anova is $$Y_{ij} = \mu + \alpha_i + \epsilon_{ij}$$ where $i$ means group $i$ and $j$ means $j$-th individual, $\{ \epsilon_{ij}\}$ are i.i.d. $N(0,\sigma^2)$. But I do not find any model equation of one-way repeated measures anova from sources like google. Yet I think it should be different from model equation of one-way anova, because the need to account for the dependency of multiple measures corresponding to the same subject.
May anyone state and contrast the difference of model equations between the two?