Electrical – What are the advantages of a synchronous switching regulator

What would be the best approach to constantly having an 8V low-noise output assuming a potential input voltage swinging between 7V and 12V? My initial guess would be to use a flyback or buck-boost switching transformer

It's a good approach. A buck-boost regulator can be implemented in a small area with a minimum component count (no isolation).

both fixed-output and variable-output regulators both require external components (diode, capacitor, inductor). Why do both require external components?

The reason is that components such as capacitors and inductors occupy too much volume when they are integrated into an IC. For this reason, they are left as external components.

I think you're a bit confused about what these parts do !

The THD 12-2412WI DC-DC converter is an isolated power converter. It is like a mini-mains adapter but with a low voltage input. It takes power from the input and using switching and a transformer makes the power available at the output. But as it is isolated, there is no electrical connection between in and output. This is useful for many applications. One field of application is sensitive measurement equipment where the sensitive input amplifier needs to have it's own isolated power supply. You could achieve the same with a battery but batteries run out which is less practical.

The TSR 1-24120 switching regulator is not isolated. Indeed it is most likely a buck converter. Note how it has only 3 pins, my guess is those are input-ground-output just like on a linear regulator. I'm also guessing that these are a drop-in replacement for a linear 3-pin regulator. As it is a switching converter, it is more efficient than an a linear regulator and it does not need a heatsink. The disadvantage is that this device will be more expensive. On eBay you can get cheap modules based on the LM2596 chip that basically do the same. But check the specs to see if it fits your needs. These more expensive TSR modules might give a "cleaner" output voltage. But it depends on your needs if that is relevant.

So both are switched converters, both are DCDC converters ! Only one is an isolated DCDC converter. Isolation requires more components and also more testing (the manufacturer wants to guarantee good isolation so they probably test it on each device, testing is expensive) making the device more expensive and larger.