Which to use where
Ok, so I've narrow the 2 main choices that you have : either a MOSFET or a RELAY. For higher voltages, it is much safer to go with a relay but for higher current, you might as well use a power MOSFET.
Option 1 - Relays
They are mainly used to control already made stuff like a bulb using main's voltage. They are also used to control stuff like a fan (pre built), lamp, and many more. Relays are also simple to wire and don't quire much electronics skills. The main disadvantage of a relay is that they are not as good as MOSFETs when it comes to current handling.
Advantages: Light bulb, stuff bought from the sotre (TVs, fans, small heater), house automation, laundry, house heater, fridge
Opition 2 - MOSFETs
IMPORTANT NOTICE : YOU CANNOT USE A MOSFET WITH MAIN'S VOLTAGE
MOSFETs are great when it comes to kick some voltage in to your devices. I remember as a kid, I use to stock these in NERF guns. Motors will instantly start with MOSFETS!. For even higher current control. Try power mosfets, they are designed for high current. Also know that mosfets are bad in the way that they tend to warm up a lot (if the current is high).
Advantages: Neon light, motors, things that need to be responsive (drone motors), things that need to be precise (PWM)
In conclusion, relays master the world of high voltages and MOSFETs the world of high current!