The terminals are the land side buildings were you enter/exit the airport and check-in for flights. The concourses are standalone structures (airside) where the aircraft dock or park and connect to the jet bridges. In some airports they are the same structure but in DXB they are not. The two are connect via underground tunnels.
I think it is confusing that there is a Concourse A/B/C and now they are building a Concourse 4. Why not Concourse D? There doesn't seem to be consistency.
Also, I don't recall going through any underground tunnels from Terminal 3 to Concourse C. Isn't the underground tunnel limited to Terminal 1?