I apologize for coming off like a Richard, if I did. The bit at the end, reguarding your age and solid-state marketing and such however has nothing to do with model trains specifically, but rather technology in general. Up until the early 50's if you wanted electricity to do more than just turn on or off the only games in town were complex mechanical devices for switching things relatively slowly, or vacuum tubes for more complex functions. Both were expensive, complex, and slow. When the transistor came along it changed everything, and the world of consumer electronics exploded with inexpensive gadgets based on it. At the basic a transistor is a power switch with no moving parts, hence the term solid-state. The term was used heavily throughout the 1960's and 70's in marketing any sort of electronic devices, especially things like pocket radios, home stereo equipment and television sets, two of which had previously use vacuum tubes and the third simply didn't exist because it couldn't be made before the transistor.
On the green wires you mention, the reason that "tiny" wires worked fine on that little set but thicker gauges are recommended when building a layout is two-fold. First, on a layout it's likely you'll be running things that take more power such as more than one engine, lighted or operating cars, electro-couplers, etc. The second is that those little green wires were really your layout is designed for without having the voltage drop very much over the length of the wire. you can plug the relevant numbers into a voltage drop calculator like this one: https://www.rapidtables.com/ca...drop-calculator.html to see what effect different gauges of wire have on high current long runs. So you have two reasons to use different wire, needing wire thick enough not to melt when using larger transformers powering more demanding equipment, and avoiding voltage drop over distance.
On the original point with transformers, the old school ones you grew up with were actually transformers in the proper sense of the word. Not sure how much detail you need since this is the sort of thing they teach kids in elementary school, but you said treat you like you're 6 years old... Two coils of wire that share a core such that when you apply alternating electricity to one coil it creates a alternating magnetic field. That magnetic field then creates electricity in the second coil of wire. As the name implies this device is used to transform the electricity. By making the wire coils different sizes the voltage and current of the electricity can be changed. For example in a common Lionel ZW train transformer 120 volts in is converted to up to 20 volts out. In train transformers the variable voltage is done with a wiper, a piece of metal that is moved by the throttle and rubs against the output side coil of wire. doing this it changes how many turns that second coil uses, effectively acting like there are more turns as the throttle is turned up, raising the voltage.
Modern "transformers" control the output voltage in an entirely different way. While they still use a transformer to convert the wall outlet's 120VAC to the max voltage of 18VAC the actual speed control for our trains is done with solid-state electronics. The actual method and parts used are slightly different than what I'm going to explain here but the basic idea is the same. (there's no need to go into the difference between transistors and triacs or what a zero-crossing is for a super basic explanation). The modern style of train transformer is commonly referred to on this forum as a "chopped wave" transformer. This is because it chops off part of the wave of electricity. As you may recall from grade school the electricity we use from wall outlets is alternating current. It "flows" in waves, up and down 60 times a second. as the wave goes up the voltage rises and as it goes back down the voltage lowers again.The voltage we read or are talking about when we say 120VAC or 18VAC is what is called RMS voltage which stands for root-mean-square. While not technically true, you can think of it as the average voltage of that wave of electricity from one wave to the next. When we measure 18 volts to the track there are actually the point when the wave is at the bottom, at 0 volts and the time when it's at the top, at close to 25 volts, but the "average" is 18 volts.
The modern transformer works by using special transistors called triacs to very quickly turn on and off the power. So quickly, in fact that they chop out parts of that wave of electricity. The math in real life is different because of the shape of the wave, but you can picture things like this: If you turn off the power half way through the wave, then turn it back on as the next wave starts, the average voltage over the time of one wave will be cut in half. if you vary where you cut off the wave it will vary the average voltage at the output. this is how modern transformers work using solid state electronics to adjust the voltage rather than a mechanical wiper physically tapping the transformer in different places.
As to the problem with connecting two modern speed controllers back to back it start with knowing that these devices have to know when the wave is starting so that they know how much to cut off. They also typically cut off the first part of the wave. So a throttle set to 75% will be missing the first quarter of the wave. The problem can come in when the second speed control device, such as a TIU is looking for the start of the wave and it sees the wave starting at that later point after it has already been chopped by the first transformer. things get confused and the wrong part of the wave gets chopped off. Basically the electronics in the TIU think they are at the start of the wave when really they are at the top, so it chops off the wrong part of the wave for the desired result. Not until one throttle is nearly all the way up do things start working correctly again.
As stated before, if you use a non-electronic transformer as the input, you won't have any problems since that post-war style transformer is actually changing the voltage, or the height of the wave, but it is still a full, un-chopped, wave that won't confuse the TIU. It just has less voltage as the upper limit.
P.S. As an entirely different discussion, since LionChief is mentioned in the title, it is worth noting that changing the voltage to the track actually has little or no effect on the speed of LionChief Plus engines. Lower voltages may cause a slow down if the engine runs out of power to suck in but for practical purposes there's no reason to run them at lower voltages. It just makes the electronics have to work harder. I seem to remember the same being true on regular LionChief engines as well, but cant say for sure, and I don't have access to testing it right now.
