Am I correct that "show pfe route ip" extracts information from PFE and "show route forwarding-table" extracts information from routing-engine copy of forwarding table? So this means that in latter case there is no RE<->PFE communication?
Correct, a little review.
The Routing Engine(s) are the control plane, they build the routing table based on all of the information given to it by whatever protocols are configured, and it also builds the forwarding table. The routing engine will then copy it's version of the forwarding table to the appropriate PFE'(s) (forwarding plane).
All in all, the RE has a copy of the routing table and the forwarding table, and all of the PFE's have their respective forwarding entries to be used to actually forward traffic.
show route- will display the routing table.
show route forwarding-table- will show the routing engine's version of the forwarding table
show pfe route ip- will show the forwarding table/entries that are actually installed in each PFE.
So this means that in latter case there is no RE<->PFE communication?
Yes, but lets be clear. In the case of
show pfe route ip, the RE still has to communicate with the PFE to query their version of the forwarding table, but it will not query its own copy of the forwarding table.
I'll be happy to update my answer if necessary.