You are right an inductor is effectively just a coil of wire. A relay is a type of switch, which uses an electromagnet (which is also an inductor). to move the switch contacts. That way, you can use a small electric current to swich on or off a larger current.
These 'relays' you speak of probably have nothing to do with traditional relays, but more like a miniature power inverter (for powering AC devices off a DC supply). They probably have a small oscillator circuit inside to produce an ac singal when they have DC power. The R and the C probably are used to set the frequency, they probably have a small integrated circuit to do most of the rest of the work.
Historically, electromagnetic relays have actually been used to build inverters: an oscillator circuit can easily be built from a relay and a capacitor and resistor (it works by using the charge and discharge of the capacitor to alternately switch on and off the relay, it doesnt work like real RLC oscillator circuits). This is how flashing turning indicators work in cars by the way, the clicking sound is the relay switching on and off! This pulsating DC current is then fed into a transformer to convert the votlage to the requried level. Modern inverters use the same principle, but use transistors instead of relays.