My you can ask some hard ones. Nah, JK, it's simple.
TCR = temperature coefficient of resistance
TFR = temperature factor of resistance
Taking it from the top: All metals conduct electricity (because they all have free electrons). Some metals are more conductive than others (copper, good; plutonium, not so much). All metals vary their ability to conduct with temperature, and in only one direction; specifically the hotter the metal gets, the more resistive to current it becomes. Some metals vary their ability to conduct very evenly across the relevant temperature scale. That is to say, a one degree temp rise between x and x+1 degrees exhibits (more or less) the same increase in resistivity as the one degree rise between y and y+1 degrees. This property is known as having a "flat TCR curve." TC mods work by measuring the resistance (technically voltage drop, which is proportional to, and varies directly with, resistance) across the coil as the mod fires, then applying an algorithm, as in "X decrease in voltage = Y increase in temperature." As the wire temp increases, the mod backs off of the power firing the coil-- usually by pulsing, but it is possible to vary the voltage-- to first achieve and then hold the set temperature. Thus, you can see a "flat TCR curve" is a good thing to have to make the TC function accurate. The flatter that curve, the better your algorithm works.
Both TCR and TFR are a means of making your TC function in the mod more accurate. The inaccuracy develops from the fact a "flat TCR curve" isn't actually flat. It's a curve (duh!). The TCR figure is a regression line (least squares linear regression, if you know what that means) drawn through the curve as plotted; a straight line drawn as close as possible to all data points. The slope of that line (in the geometry sense) is the TCR figure. Having a TCR mode on your mod permits you to tweak the factory set TCR for the wire you select. Perhaps you are using a different alloy than the mod thinks. For example, 316, 316L, 317 and 317L grades of Stainless Steel will all work on your mod in "stainless" mode, but in reality they all have (slightly) different TCRs. You can select the proper TCR in the TCR mode, a thing you can't do in stainless mode. Another thing this can help with is if you mod's measuring circuit is not quite properly calibrated. You can mess with the numbers a tiny bit to move the TCR curve up or down the scale to raise or lower the heat of the vape (not that this is necessary unless you are a tinkerer as simply adjusting the set temperature does the same thing).
TFR mode is quite similar; a means of accurizing the TC function. The difference is simple. Where "TCR" uses a straight regression line, "TFR" permits you to enter the actual data points at several-- the ones I've seen or read about is 5-- temperatures. This allows the mod more data to work with. Instead of a single straight line indicated by its slope, it gets multiple data points between which it can interpolate, theoretically resulting in greater accuracy.
I hope that hits the high spots for you. For me, I gave up on TC a long time ago. But then, I don't really need it. I am a coil builder and I know how to make the mod do what I want anyway.