For example.
R1 is RP
R2 -- DR
R3 -- source's router
R4 -- receiver's router
R1, R2 and R3 in LAN1
R2, R3 and R4 in LAN2.
JOIN (*,G) will keep traveling R4->R2->R1 path to RP.
JOIN(S,G) will travel R4->R3 path right to the source network so R3 will become a forwarder.
RP tree and SP tree are two different trees. RPT root is RP and SPT root is source's router. As soon as R3 receives first multicast packet it joins as leaf to SPT for the source of received packet and prunes from RPT for this source when SPT to source built and traffic flows over new path.
In case ssm join received by R4 it might omit RPT phase and start directly from SPT.