It's about their output impedance. These sources are pretty much the same thing, but we call low impedance sources "voltage sources" and we call high impedance ones "current sources".
Example
Take a 12 V car battery. ItBy itself, it is a reasonably good voltage source, because its internal series impedance is low for most purposes. Its output voltage would be always about 12 V, regardless of the load.
Now add a 1 MΩ resistor in series and suddenly it is a reasonably good current source, which will output a current of 1.2 µA through most loads. But it's output voltage would now be highly load dependent.