Conneting nodes does not necessarily mean that two nodes are at same pt. in space.
It simply means that the two points are connected in the specified degree of freedom ( say ANC, X, Y, Z etc) by the specified stiffness [ if default stiffness is used then the node-C-Node are not having any relative desplacement in the connected DOF but can have relative displacement in the non connected DOFs. If however non rigid stiffness has been used, the node, C-node can have relative displacement even in the connected DOF(s)].

A simpler way to look is like this: A point w/o C-node is also having a C-node which is immovable in space say , ground . For a node having a C-node the point is moving and not immovable in space.

Suppose a pipe is supported from ground , this is a case of " no C-node".

Similarly if a pipe is supported from a pipe support clip welded to a vessel that point is not immovable like ground.

Mathematically C-node is an application of an FEA concept of " Multi Point Constraint".

There are enough examples in CAESAR II manuals to explain this concept.