Coach screw - tapered screw thread, hex head. Screw thread may be all or part of the shaft. To screw into material.
Coach bolt - parallel thread, along all or part of shaft, to be secured with a nut. Head may be hex or domed - or is one a carriage bolt?
Some coach bolts have slotted heads - as used in greenhouses?
Some have a square rather than hex head.
Then there were bolts to attach car chrome bumpers. The heads were less domed. Think Anglias, Cortinas etc.
Doubtless there are permutations I have forgotten, or never noticed.
Are they all coach bolts, except the ones that are coach screws?