Most microprocessor manufacturing (along with countless other devices) undergo the process of binning: all similar products are made at once, and depending on their performance, are placed into "bins" (groups) of similarly performing products, and then packaged and sold accordingly.
In the case of Intel processors (AMD is similar), generally processors within the same line are manufactured together, and are binned according to their stable clock frequency. You can tell when a processor is part of the same "line," by looking at the core codename, or if that is not specific enough, the features of the core (as mentioned by embedded.kyle, the i5 doesn't have hyperthreading, but the i7 does, even though both in question are "Sandy Bridge").
Sometimes a higher-end processor that fails can still be sold as another. An example I know first-hand is that the M0 steppings of the old Northwood-core Pentium 4's (130nm process) were actually failed Gallatin-core processors (which was the core for the P4 "Extreme Edition"). Similarly, a lot of people had/have luck unlocking extra cores, caches and shader units on various CPUs and GPUs. For example, it is quite common to be able to buy a mid-high range video card (take for example, the AMD Radeon 6850) and flash it with the BIOS of the higher-level card (the Radeon 6870, in this case) and gain the extra things that card has (some extra shader cores). This also has to do with binning during the manufacturing process.
This sort of thing drives overclockers to take good note of the stepping, place of origin, and batch number of their processors. When word gets out that certain batches of processors are overclocking better than their not-as-potent brethren (same CPU, mind you, just made at a different time or place), they become more in demand.
If you're interested more, definitely search "CPU Binning," or read up at some forums. I'm a member at www.overclockers.com, and the forum there is quite welcoming and has a wealth of past and current knowledge (along with an abundance of fantastic members).
Am I correct that the faster processor draws more power (and thus
dissipates more heat) under a computational load?
Not necessarily. There are two major components of power dissipation - static power (the power you burn when the chip is on) and dynamic/switching power (the power burned when the clock is running). While running the same chip at a higher frequency will result in more power dissipation, a chip may have a static power dissipation that is too high when combined with the faster clock rate to meet the bin requirements for the faster rating.
If so, is the power under computational load approximately
proportional to the rated/clocked frequency? In other words, inasmuch
as the one processor is clocked 8 percent faster than the other, does
it run about 8 percent hotter under load? Another way to ask the same
question is to ask: does each processor process about the same
quantity of data per unit of energy? or, if battery powered, can each
accomplish about as much before its battery dies?
For a given chip running identical calculations, the dynamic portion of the power consumption will be proportional to the clock frequency. The total power dissipation of the processor will increase a bit less than 8% for an 8% increase in clock frequency due to the static power dissipation.
When not under load, do the two processors idle equally cool, or are
there practical or theoretical factors that make the one idle cooler
than the other?
If you had two identical chips idling, the one with the lower clock frequency would dissipate less power. When the chips are idling, the static power becomes a much larger portion of the active power dissipation, so any differences there would be more noticeable.
Even if the processor's price were not determinate, might one prefer
the slower processor merely for the sake of cooler operation and
extended battery life?
Possibly, but again, you have a lot less of a guarantee that this would be the case. If you bought chips with different rated TDPs, then you could safely make this argument. Otherwise, you're at the mercy of the binning algorithm and the consistency of the manufacturer's process. Also, note that we're talking about power dissipation, not energy consumption. A faster processor may be able to complete a computationally heavy task faster, and switch to a low power idle mode sooner than a slower processor.
Would the answers differ for embedded processors?
Yes. The static power dissipation is most significant on the bleeding edge processes that Intel, TSMC, IBM, and Global Foundries use. Embedded processors are often optimized for low static power dissipation and use larger processes where static power dissipation is a much smaller portion of power dissipation. The variation at those larger process nodes is much less, so microcontrollers are much less susceptible to variation in power and frequency performance.
Best Answer
Look at Freescale's comparison page. I believe all of the models you listed are in the table. They vary by cpu/bus clock speeds and min/max operating temperatures.