There is a lot of philosophy in this matter... and it can be revealed through generalized rather than specific explanations because the problem is purely electrical. Specific electronic implementations can only serve as examples that illustrate the general idea.
Logic gates, like most electronic circuits, are voltage controlled. The problem is that, in many cases, we do not know what is inside the input. It can be "floating" (MOS gates) or connected by a "pull-down" element to ground (BJT gates) or to Vcc (TTL gates).
Voltage source. So, input sources (previous stages) should be controlled voltage sources producing voltage with two possible values - HIGH and ZERO. In both cases, the source output resistance has to be zero; so ZERO means both zero voltage and zero resistance. This will ensure that we apply the desired voltage to the gate input.
This requirement applies not only to digital but also to analog circuits. If it is not implemented in most cases, circuits simply will not work. For example, if in a RC differentiating or integrating circuit we apply zero input voltage by disconnecting and not by grounding, the capacitor will be constantly charged and the circuit will not work.
Complementary stage. Such a "true voltage source" is implemented by two complementary "pulling" elements - a "pull-down" element between the output and ground, and a "pull-up" element between the output and Vcc. They can be thought of as "ideal" switches connecting the output either to ground or Vcc... but actually they can not be "ideal". Let's see why.
The problem is that they should not be both on to avoid a short circuit. But they also should not be both off (even for a while) since the output will be "floating" during this time. Therefore, they must be oppositely varying (cross-fading) resistances to allow overlapping. So the input "voltage source" consists of two complementary (pull-down and pull-up) voltage-controlled "variable resistors" (transistors). I have considered this problem in my answer to a related question.
Open collector stage. If there is such an (e.g., pull-down) element inside the logic gate input, we can control it by only one (pull-up) element. This is the so-called sourcing "open collector" output. And v.v., if there is a pull-up element inside the logic gate input, we can control it only by a pull-down element. Now this is a sinking "open collector" output.
The general conclusion is that, to control a logic gate by voltage, there are always two complementary "pulling" elements. In the case of complementary output, both are inside the output of the previous logic gate. In the case of the "open collector" output, one of them is inside the previous output and the other is inside the input of the next logic gate.