How does a boost pedal work?
Mission Engineering has a fantastic explanation: "it takes the low level output from a guitar pick up and increases it before passing on to the next part of the signal chain. The number of times the amplifier can increase the output power over the input power is referred to as the gain."
What is the difference between boost and gain?
Boost increases the volume without necessarily changing the tone. Gain impacts the tone. Gain is typically associated with overdrive or distortion.