So I heard from Jerry that there was a conversation about forge welding copper over here. Yes you can forge weld copper, it needs to be kept clean and in a strong reducing atmosphere while heating. It can be tricky as the oxygen in the air will cause the bond to fail if it gets too much exposure. This is why it is easier to make the weld in a mokume type of fixture. Also the more deformation (spreading) of the bonding surface you can get on the first strike the better your chances of a successful bond. It is not an easy weld but having a big power hammer will make it easier.
As for welding definitions, forge welding, mokume, pattern welding (damascus) are all solid state welding. TIG, Stick, torch etc are all liquid phase welding. Both types are true welding, but there are metallurgical differences in the crystal structures resulting from the joining.