What is RRCConnectionResume-r13 in LTE?

It is the downlink LTE RRC message the network sends to accept the resume of a suspended LTE context.

What comes after RRCConnectionResume-r13?

The UE normally responds with RRCConnectionResumeComplete-r13.

How is it different from RRCConnectionSetup?

RRCConnectionSetup creates a new connection. RRCConnectionResume-r13 restores a suspended one.

What should I inspect first in RRCConnectionResume-r13?

Start with whether the branch is really a resume path, then inspect the resumed dedicated configuration and the following completion step.