Paired sample t-test and Repeated Measures ANOVA with a dichotomous predictor are two tests that answer the same question, and output the same p-value as far as I can tell.
This question has been asked before, but it was focused on the assumption of both tests. What strikes me more here is that the test statistics are different: one is based on the $t$ distribution while the other on the $F$ distribution. Is there any theoretical way to explain why these two distributions should be close to each other in the case of a dichotomous predictor?