Was your last birth natural? From what you have discribed it sounds like an in-out catheter (or intermittent catheter) was used (if it was placed in to drain then removed straight away - done a number of times etc). these are considerably shorter and firmer (often silicone or a pvc) as they are often designed for self-catherisation and it makes it easier to be used by the lay person. It is a possibility they used this type of catheter during a normal labour (no spinal/epidural for c/s) as it eliminates having a longer term catheter in place which may get in the way down there and therefore causes a problem with sterility.
Yes it was an in and out again situation, used to drain an overly full bladder so bub's head had room to move. It was definitely firmer or straighter, and felt quite hard (and sharp) going in. For some reason I thought it was put in with the wire that was then removed, although it's possible in my haze I have gotten the wire bit confused, since there were a number of sharp wirey things poked into me on multiple instances (three different drs had about a dozen tries at ARM before concluding the membranes were "probably" broken) and then later on a similar story with trying to get a scalp monitor attached to DD's head.

I'm not at all concerned about the catheter for the CS -it looked a lot softer and less scary, and if anything I'm looking forwards to not having to trip to the dunny to pee constantly!