There are two types of thermal fuses. The hair dryer version is set for a specific temperature and pop. This is usally accomplished by using an alloy that melts at that temperature.
Every fuse is essentially a piece of wire that is designed to melt in a nice enclosed space. There are various forms of ohms law, such as P=I^2*R where I would be the current and R, the resistance of the fuse. Furthermore R=pLA of a material which hass a material constant Rho, a length L and a cross-sectional area A.
The time that a certain amount of heat is applied raised the temperature assuming no losses.
So, fuses are designed to handle 100% of the current for an infinite time. 110% and 300% will have different blow characteristics. Fuses are designed to handle short circuit protection. e.g. Don;t allow more than 15A continuous through this wire in your house, otherwise the wire will get too hot and bad things will happen.
PolySwitches are basically designed to protect motors and battery packs and they will likely reset on their own. When a motor starts, it nearly looks like a short or the value if the resistance of the windings. If the rotor doesn't move, the current is limited by the resistance of the windings. How long it doesn't move creates heat. So, the poly fuses will allow the motor to see a large load "briefly" but would cur out when it occurs for a longer time than a fuse.
Time-delay fuses are typically used for motors. In an industrial setting "Thermal fuses" are also used. Sensors are also used at the motor.