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I know that it is unwise to use 14 awg wire on a 20 amp circuit and that 12 gauge should be used because the larger wire can handle the larger load, right? Then how come when I open up a night light (that can be plugged into a 15A or 20A circuit) I find tiny wire (18 gauge?) coming directly off the plug pin to power a little LED bulb?
In other words, why can electrical devices use such tiny wires inside if they're on a regular 15A or 20A circuit?
Circuit wire is kept relatively large because general purpose receptacles are just that: general purpose. You can plug a nightlight into them one moment and a kilowatt hairdryer the next.
In a fixture, luminaire, or appliance, on the other hand, the designers can use thinner wire (down to 18AWG for fixture wire as per NEC 402.6) as they know how much current will ever flow through there -- the appliance or fixture only needs a certain amount of current, never more (unless there's a fault, which is why you have fuses in appliances).
The wiring in the wall (12/14awg) is sized to handle the entire capacity of that circuit up to 20/15 amp. The circuit will regularly include multiple lights or outlets within it.
The circuitry within the light you mentioned only needs to handle the capacity that that device will use. If you open a device with a larger power draw (blender?) you will notice the wire is closer to the 14awg or if very high draw (range?) you could see 12awg or larger conductors.
Metaphorically: Think of it as a tree, you don't need a tree trunk to support the weight of a single leaf. But when you combine two dozen leaves you need a branch and when you combine two dozen branches you need a trunk.
