Thermosets are most frequently used in situations where the part must be able to withstand high temperatures. Medical parts are a good example; dental tools with silicone handles and metal parts must be able to withstand the autoclaving process in order to be sanitized and reused over and over again, so the silicone must be thermoset. Higher voltage electrical applications also use thermosets.
Thermoplastic parts are more likely to be used for consumer plastics that either won’t come in contact with high temperatures, like the plastic used in milk jugs, or will need to withstand moderately high temperatures. Certain polycarbonates, for example, are resistant to hot liquids and often used to make plastic to-go mugs—but they can still deform or melt at high-enough temperatures.
When considering thermoset vs. thermoplastic parts, you’ll also want to consider whether the part will regularly be contact with certain chemistries. If you’re manufacturing plastic casing for an EKG, for example, the material used will need to be able to withstand any hospital-grade chemical disinfectants.