What's the difference between these components?

Well, the thing about electricity is- it's more than just volts and amps. Power-AKA heat and thermal considerations comes into play.

If you are conducting both voltage and high amperage, the losses heat the component. It must then transfer that heat to something else- heatsinking- in order to not overheat and thermally break down.

The barrel style epoxy covered diode uses the legs (the metal wires) to transfer heat from the diode junction- hence they are thicker wires to help transfer that heat typically to the circuit board and it's copper traces.

The stud mounted diode is meant to attach to a heatsink directly, thus handling far more power (again voltage times current).

Again, a diode has some level of voltage drop across the junction- that drop= heat. How much heat is dependent on the current and the higher the current, there is slightly more drop and more heat.

@Ted S posted:

  When would you use one, relative to the other?  Thanks in advance for sharing your wisdom and experience!

Example, let's say a large heavy duty electric forklift battery charger. It's going to be used for hours, often overnight or all day charging a huge set of batteries. In that case, I'm going to use stud mounted heavy duty diodes rated for that kind of heavy duty long lifespan thermal load.

Now say I'm building a train control circuit board like a PS1 lower power and control board. Nowhere near the load and thermal heat buildup, but also, I do not need the huge power handling and size of a stud mounted set of diodes.

In our common usage, you may see those diodes used inside an old postwar ZW transformer. Either type could work, some opt in for the larger stud mounted version because there is more space and the ZW can output a fair amount of current in the short term, so a big beefy diode is not a bad thing. But others are perfectly happy using the smaller barrel type and given only being used for whistle function intermittently, it's well within the thermal scope.