Why do resistors in series have different potential and a common current and resistors in parallel have different current and a common potential throughout?
There is only one path for the charge in the series circuit that's why it has to go through the same path(because the charge is conserved in nature) So the current remains the same in a series circuit due to conservation of charge.
Potential across the resistance is the product of current and resistance so if the resistance is different in series combination the potential across the resistance will be different.
In a parallel circuit, there are more than one paths between two junctions (nodes). So the current can divided into different values and because all paths are between two fixed junctions(nodes) so we can say the potential between all resistance is the same.