I think Elizabeth is right (see her response) -- you are diving too much into the nitty-gritty details without having a good idea about the high-level concepts. Let's try one more time. The following is a gross oversimplification.Atoms are formed from positive protons and negative electrons. Protons are relatively big and slow to move -- electrons are relatively small and nimble.Each proton has 1 positive (+ve) charge. Each electron has 1 negative (-ve) charge.In some materials like rubber, the atoms hold onto their electrons tightly -- these materials are insulators.In other materials like copper, the electrons are more loosely attached -- if you push an extra electron in one end, it will push the next electron out of the way, and this will "ripple down the line" until an electron pops off the other end of the wire.It's possible to create materials that have a lot of positive ions (that is -- more protons than electrons). It's also possible to create materials that have a lot of negative ions (that is, more electrons than protons). You can think of a battery as being formed from two containers -- one containing positive ions and the other containing negative ions -- with an insulating barrier between them:
Let's say the negative side of our battery is at 0V and the positive side is at 5V -- if we connect a conducting copper wire between the two ends -- the small feisty electrons will race through the wire from the negative side of the battery to the positive side:
Note that the reason we usually show the arrow (representing current) going the other way is that the people who wrote the first books and drew the first diagrams ~150 years ago didn't really understand what was happening (they didn't know about the existence of protons and electrons per se)I think the main reason for your confusion is that you keep on saying (incorrectly) that the wire has "no resistance" -- if this were true, then I guess you could say that all points on the wire measure the same voltage -- but only for a very short time before everything exploded.The equation that describes the relationship between voltage (V), current (I), and resistance (R) is V = I x R. So I = V / R. Now, if R is 0, then anything divided by 0 is infinity, so the current would be infinite and you would experience a very big bang.In fact the wire does have resistance, even if it's very small. One way to visualize this is that the wire is made up on a long line of small resistors. Let's suppose we had only 4 such resistors as shown below:
If we use a multimeter to measure the voltage at the negative side of the battery we will see 0V -- if we measure the positive side of the battery we will see 5V -- if we measure between the two middle resistors we will see 2.5V -- and so on.Now imagine that the wire is composed of millions of these resistors -- but each one is really, really tiny.So -- if you just connected a pure copper wire between the battery terminals -- theoretically you could measure different voltages all along the length of the wire -- in practice this isn't going to work because your battery will melt before you've managed to pick up your multimeter.Let's suppose we are dealing with an ideal (no internal resistance) 5V battery and we connect the two ends together using 3 inches of 24 AWG (American Wire Gauge) wire -- using this calculator (https://www.cirris.com/learning-center/calculators/133-wire-resistance-calculator-table) we see that the resistance of the wire will be 0.006 ohms. So, using V = I x R, I = 5V / 0.006 ohms, so I (current) will equal 833 amps.Since power P = I x V, this means you will be burning more than 4kW of power -- which means your battery just turned into a pile of smoking chemicals.But if you replace the four resistors in the previous diagram with four 1k ohm resistors, then your current will be 5 / 4,000 = 0.00125A, which is no problem -- now you will be able to use your multimeter to see the different voltages at different parts of the wire.
