An ideal voltage source has zero internal resistance, which allows it to distribute all of its voltage perfectly across a load within a circuit. In the real world, a voltage source often has a very low, but non-zero internal resistance, as well as an output impedance.
However, this is typically less than 1 ohm, so it is close to the ideal source with zero resistance. As long as there is sufficiently low impedance within the load connected to the source terminals of the circuit, a current source will provide a constant current.