Understanding the meaning of a waveform of an alternative current
No, that is a plot of current vs. time (at least, if I understand what you're asking). In electrical engineering, most of the plots you will see of current or voltage are with respect to time (because that's the dimension we care about).

It's not really possible to have a wire with a varying current along its length (alright, so that might not be technically true, but for the purposes of this discussion let's say it is). Kirchoff's law tells us that the current into a node must be equal to the current out of a node. Pick any point on the wire and let that be our node. Then the current in must be equal to the current out, and therefore the current in a wire must be constant along its length.

It's worth pointing out that this is true for "conventional" cases (low frequencies and well-behaved wires). In the context of very high frequencies, everything falls apart.