For instance, we applied Pettit test and Sequential Mann Kendall test for change point detection in streamflow series. The results from both the tests did not match each other. I referred some other literature also, they also reported non-conformity in change points from these two tests. So what could be the interpretation or the way out in such a situation?

Now change point detection could be in terms of shifts in mean, variance, trends, mean and variance both, mean and trend both, etc. in a time series. So are some statistical tests specific in determining one of the above type of change/shifts in the time series or universal in application?