According to vehicle dynamics, there appears to be two different ways a wheel travels a curved path. I don't think this requires an expert in vehicle dynamics because it is a simple physics problem of a rolling wheel changing direction.
The figures below examine the path of the front wheel of a bicycle as the rider counter-steers and proceeds through a left turn - Figs 1A-1D. As the bike rolls, there are periods when the rider is turning the front wheel and periods when the rider holds the front wheel at a fixed angle - Figs 2A-D. During the “wheel turning” periods, which are shown in red, the front wheel follows a curved path. Here, the wheel changes direction by rotating/turning about its contact point. Pretty simple stuff because it’s easy to understand how turning a rolling wheel results in curved path travel.
During the periods where the front wheel is fixed at an angle, which are shown in blue, the wheel also proceeds through a curved path. We now say the wheel proceeds through the curved path by a different mechanical principle and no longer turns at its contact point to change travel direction. Since the wheel directions are fixed, we think they turn about a location other than at each contact point. We believe both wheels are tangential velocities rotating about the turn center - blue paths in Fig 3.
How can the front wheel change travel direction by rotating about its contact point (red paths) and then mysteriously change the way it changes its travel direction (blue paths)?