As the title said, I do not make the difference between port-channel and etherchannel. For me they both aggregate ports in an Ethernet networks using Cisco parlance.
What subtlety do I miss ?
"EtherChannel" or "Link Aggregation" is the particular technology that allows you to bundle several links between two devices and use them simultaneously as a single interface.
"Port-channel" is the name of this virtual interface in IOS. This is similar to, say, WiFi as a technology, and "Dot11Radio0" as the name of the interface, or ISDN as a technology, and BRI as an interface name.
There can be similarities in the actual command used on Cisco IOS or Nexus NX-OS to show a summarized list of Port-channels, for instance, on IOS the command is:
show etherchannel summary
Where on NX-OS, the command is:
show port-channel summary