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Newbie doubt regarding battery voltage


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I've recently started with electronics as a hobby, thanks to Arduino. It looks I've some misconceptions about battery voltage supply, and I'd appreciate somebody clearing this up for me.

I've a battery that's supplying around 9.3V (when I connect multimeter to the two terminals without any load, it measures around 9.3V).
I assumed this battery will always supplies 9.3V to any circuit.
However, when I connected a 220ohm resistor and an LED in series, and measured voltage across the two wires connected to battery terminals, I found it to be just 3.23V.
When I removed LED and left only the resistor plugged in, I got just 2.25V.
Why is this? Why isn't it always 9.3V? Does voltage supplied by a battery depend on the load in the circuit?

I also tried this by replacing the battery with Arduino, and using it as a simple power supply. I plugged in the resistor and LED in series into  the 5V and GND analog pins. Voltage across the leads running into the pins measured 5V as expected. I removed the LED from the circuit, and it still measured 5V. I expected the battery supplied circuit to work like this, but it didn't. Is it that Arduino outputs a constant 5V voltage always, regardless of  the load in the circuit?


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