Electrical – What’s the difference between these wires

I would use metal boxes. Much more sturdy and not very much different in cost in the grand scheme of things.

You mention that aluminum wire was used to the stove. Was that aluminum wire fed all the way back from the main power panel? If so then you'll likely have an electrical box with a receptacle mounted to it that connects to the AL wire. Make sure to purchase a socket assembly specifically designed for deployment with AL wire. (That is of course unless you will be replacing the feed wire back to the panel with copper).

Unless the new dimmer is specifically marked with LINE and LOAD or similar, it doesn't matter which wire goes to which screw/pigtail in a simple two wire switch or dimmer. Since your new switch can be used as a three way, the instructions should say which screw should not be used.

Some electricians will follow a standard of the hot wire going to the top screw and the switched wire going to the bottom, but that's just so they personally know what they did and not a "rule" or "code".

Edit based on comments:

Here is a diagram that I believe is for your dimmer:

They do specifically call out a screw for Line and a screw for "single pole" operation. Now, the dimmer might work regardless of how you hook up the two black wires, but, they warn than the dimmer needs to be wired this way, so we really should listen to them.

With the old dimmer removed you can separate the two black wires in the box and make sure they are not touching anything then turn the power back on. Using a voltmeter you can check the voltage between the two exposed black wires and ground or neutral. The LINE wire will be the one with voltage (~120v). The wire going to the lamp will be dead. DO NOT touch any wire until the power is turned back off, or call an electrician if you are not comfortable making this measurement.

Based on the diagram, the wire that had voltage goes to the "common" screw and the wire to the lamp (that had no voltage) goes to the "single pole" screw.