At first glace, the circuit you show looks a lot like a single channel of a ULN2003A 7-channel Darlington driver. Sticking with the ULN2003A, each of its channels uses a Darlington driver, a circuit where one transistor directly drives another transistor to get a combined current gain higher than the current gain of a single transistor. The COM diode in each channel is useful if the 7 open-drain drivers are each switching an inductive load, like a relay or a solenoid, and all 7 loads run from a common supply. Then the diodes are used to clamp the back emf of the inductive load.
With that to one side, let's answer your actual question...
Open-collector is a type of switched load driver circuit, along with open-emitter and push-pull. Open-collector and open-emitter are used if the switching component is a bipolar junction transistor (BJT) as collector and emitter are terminals of a BJT.
If a FET is used as the switch, the terms open-drain and open-source are used as those are the relevant terminals on a FET.
In a switched driver, the output transistors are either switched hard on or switched hard off, never partially conducting. They can be seen to act like simple on/off switches. In actuality, there's a lot more to the circuit behaviour than that simple summary but it lets us grasp the basics of what it does.
The comprehensive switching driver circuit is a push-pull output. This consists of two switching transistors - FETs in the example below.
Here, when one FET is on, the other one is off. As the diagram shows, this circuit has two driving states. (1) When the upper FET is on, the lower FET is off and the circuit is driving (supplying) current to its output at a 'high' voltage. (2) When the upper FET is off, the lower FET is on and the circuit is sinking (taking) current from its output at a 'low' voltage. Ideally, the 'high' voltage would be VDD and the 'low' voltage would be GND but the imperfect FETs have losses so not they vary away from that.
An open-collector driver circuit contains the lower transistor that sinks current but has no upper transistor to supply it. Those names are for a BJT circuit. When FETs are used, it's an open-drain driver circuit. As shown below, the push-pull FET circuit (left) has had the upper FET removed (middle). When the lower FET (middle) is on, current can flow through the transistor to GND. When the lower FET is off, there is no current flow and the output is said to be 'floating' or at high impedance. An external circuit must supply the current to flow through the lower FET. This could be a pull-up resistor (right).
Similarly, the open-source driver FET circuit has an upper transistor and no lower transistor. It can supply current to the output or be high impedance.
All three driver circuits are illustrated in these FET circuits.
There is plenty more you can read up yourself on the internet on these circuits. This should give you enough of the basics to find, understand and learn.