TP vs R3TRANS
Nature wise no difference both are tools included as part of kernel. Functionality wise they are different - R3trans is used for DB<>SAP connectivity and tp is used for transports. R3trans depends on OPS$ mechanism for the connectivity and TP depends on domain controller and subsequent profile of the same to do the transports.
TP - "The Transport Tool". This program coordinates the complete import and export of program and table changes made within the SAP system in order to transport them through the complete System Landscape. TP is a transport program and R3trans is a tool for transport. So here TP uses the R3trans for transport. TP means It is calls to R3Trans only. R3Trans is moving the transports.
R3trans - This is the tool, that does the real work for TP. TP controls the import and export of changes and R3Trans does them using scripts, that were generated from tp.
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TP is a transport tool used to control the import and export of program and table changes made within the SAP system in order to transport them and R3TRANS does them using scripts, that were generated from TP.
In short R3TRANS is the tool, that does the main work for TP by initiating it to transport file from OS to DB and vice versa.
TP controls the process and calls several tools, like R3TRANS but also e.g. DDIC-Activation.