Word for relative movement of inner and outer

Solution 1:

I would say displacement for the distance traveled. (Independently from Carl Witthoft.) I can't think of a word for the act of moving, but since this is happening in a 1-dimensional manifold, motion suffices: the motion of the object through the tube, or the relative motion of the object and the tube. From time t to time t', there is a displacement of 3mm in one direction.

If the object can also “wiggle” inside the tube, this wiggling would be radial motion. Motion alongside the tube is axial motion.

_{Warning: I am neither a native speaker nor a physicist.}

Solution 2:

You could consider the verb snake, which means to move, twist or wind, to make a course through (in the manner of a snake).

It's not immediately obvious from the definition that this is a fit, but some examples come to mind that are similar to your example:

He snaked his way through the surrounding crowd.

You clean your saxophone by first snaking this string through it and pulling the attached cloth all the way through.

Snake this auger through the pipe to clean it.

The optic fiber was installed without disrupting traffic. We simply snaked it through an existing utility conduit that ran between the two sites.