Yes you're right.
As far as I can tell (checking Machinery's, Molesworth, Caxton and Spon) a cotter is a key distinguished by having two shear planes, not just one
- i.e. it goes right through something, out the other side, and the external ends are supported in two places.
They're usually tapered. This is a convenient way of locking them in place and it allows both sides to be tightened up, allowing a reciprocating force without fretting damage. In a locomotive big end there's a cotter which may or may not be tapered, as it's tightened by a separate tapered gib strip.
If there's no taper though, it's difficult to get a cotter tight against forces on both directions. This would only be useful if the load was guaranteed to only act in one direction. The only example I can think of are the suspension cables (not the catenaries) of a suspension bridge - sure enough there are plenty of Victorian pnes that use plain cotters here.