It's a terminology issue more than anything, the descriptions are from the module's perspective; "Echo Output" is an output from the module so goes to a PICAXE input, "Trigger Input" is an input to the module so comes from a PICAXE output.
On the PICAXE side it would be sensible to label the two connections as "Echo Input" and "Trigger Output", then it becomes clear that an output from one is an input to the other.