Capacitor as voltage source but why not as current source
When we describe something as an (ideal) 'voltage source' or 'current source', we are really describing its behaviour when we connect it to a load. 

In particular, we do not mean that a current source only supplies current and not voltage, or that a voltage source only supplies voltage and no current. Actually both kinds of sources can supply voltage and current to a circuit. This seems to be a surprisingly common misconception.

For example, if we have a voltage source of e.g. 9 volts, and we connect it to a resistor, the voltage across the resistor will be 9 volts. On the other hand, the current through the resistor depends on the resistance according to the equation:
$$ I = \frac{9}{R}$$
if we change the resistance, the current will also change according to this equation, but the voltage across the resistor will remain at 9 volts. So a voltage source supplies the same voltage across any load.

If we connect a current source of 2A to the resistor instead, then the voltage across the resistor depends on the voltage according to the equation
$$
V = 2R
$$
but the current is now fixed at 2A. So a current source supplies the same current across any load.

For a capacitor charged to e.g. 5V, when we connect it to a resistor we find that the voltage across the resistor is 5V and the current through the resistor is:
$$ I = \frac{5}{R}$$
If we were to try this with different resistors, we would find that the voltage across the resistor would always be 5V but the current would change depending on the value of the resistance. This is the same behaviour as our ideal voltage source, so we say that the capacitor behaves as a voltage source. 

Of course, in practice capacitors tend to discharge quickly and the voltage would then drop over time, so the discussion above only really applies to the instant of time immediately after you connect the circuit. However, even though the capacitor voltage drops with time as it is discharged, we still find that it supplies the same voltage regardless of the value of the resistor.