There are rumours of a musical instrument called a hornpipe but you don't see many of them around. I'm very dubious about the authenticity of the Highland Hornpipe as a traditional instrument, but it may be based on somthing that did exist once.
Early hornpipes could have been bagpipe tunes, though many surviving example even of the earlier 3/2 hornpipes have too much range for a bagpipe chanter. That may be because they were modified by fiddlers later. The later common time hornpipe appeared in the 18th centrury and was likely to be played on fiddles and other instruments, but the name may have survived from the bagpipe days.
There's an article by Gavin Atkin in an earlier EDS with a theory that the Naval hornpipe (dance) was derived from the step dance still found in East Anglia and Dartmoor.
The "Trumpet" Designation is of course from the opening triplets of that particular tune, and the Pugwas Theme was a recording of Northumbrian accordionist Tommy Edmondson.