There's voltage and there's current, like in a pipe/water analogy there is pressure and there is .. current ("amount of water passing through a cross section in a unit of time") in a pipe. Both are important and linked.
There's also voltage sources and current sources (current sink is a source pointing in the opposite direction). Ideal voltage source (think 9V battery) provides whatever current is consumed by the circuit, keeping its own output voltage constant. Ideal current source provides whatever voltage is needed by the circuit, keeping the current constant. Real voltage and current sources have limits, non-linearities and impedances to think about, but that's going one level deeper.
Now what does it all mean practically.
If we want to analyse how for example an inverting amplifier configuration works, we need to look at both voltage and current (see Aaron Lanterman's video on opamps). But once we have analysed it we can simplify the inverting amplifier and say that it's just a voltage-controlled voltage source with a certain input and output impedance. Meaning that ideal opamp will source whatever current is necessary so that we can see a certain Vout on its output that would depend on Vin.
That's the level I have been thinking about circuits before (everything is a voltage-controlled voltage source). That's also partially the reason everyone is more comfortable with opamps compared to, say, BJTs.
Now not everything can be modelled as a voltage-controlled voltage source. BJT is one example of a transconductance device. It's a voltage-controlled current source. Meaning that it would create whatever voltages necessary to keep the collector current constant.
We take advantage of that when we hook up a BJT as a common-emitter amplifier, so collector to a voltage source through a resistor. One leg of the resistor is looking at the voltage source, another is looking at BJTs collector that's sinking current. The amount of current that it's sinking is controlled by the input voltage at the base. The more current is sank through Rc the more voltage drop we see across it. That's how we convert current into voltage and get our "amplified inverted input voltage" at the collector.
So confusingly common-emitter BJT configuration is like a voltage-controlled voltage source. But that's only because the collector is looking at a voltage source and we convert "current sank" into voltage using that collector resistor.
If we connect a collector of a BJT to a capacitor for example (like with oscillators) it would sink or source a constant amount of current, that will be controlled by a voltage at the base. Giving us a voltage-controlled current source and resulting in a linearly increasing / decreasing voltage at the capacitor. That's because as we linearly fill something up the pressure (voltage) with which it's pushing back increases linearly.
- Changed "common-collector amplifier" to "common-emitter amplifier", always confuse those.