The two circuits are not the same. The original is a wheatstone bridge circuit and is in the standard schematic form for such circuits.
To be equivalent all resistor junctions must go to their original locations. For example, in the C2 schematic, R3 and R5 are in series with no other connection between them. The original circuit has R4 connected to the junction of R3 and R5. If you remove R4 from the connection to R2 and, instead, connect it to the junction or R3 and R5, then the two circuits will be equivalent.