If there's no inductor (and inductors are dangerous: see my other comment), then nothing on that PCB is pushing any current. Its all illusions created by "pulling" current.
> but you can of course design a circuit that will adjust voltage to keep current constant
So there's two designs and they're different in important ways. But first: the common part of _both_ designs is that the transistor is working as a "controlled resistor". The question is where you place this special resistor. The other commonality is that "negative-feedback" can configure this transistor to reach the appropriate resistance very easily.
So with the common stuff out of the way: we have two designs. "Series Regulator" and "Shunt Regulators" (traditionally voltage-regulators, but they could be current in practice. I'll discuss as if they're current regulators).
1. Series Regulator -- The transistor is treated as an adjustable resistor "in series" with the rest of the circuit. This "pinches down" the voltage/current to the level deemed acceptable to the engineer. Ex: If "downstream", you sense a 100-Ohm load and you have a target-current of 10mA, and your source voltage is 5V, you set the transistor so that its equivalent to 400-Ohms (total a 500-ohm system, so 10mA goes through).
But if the downstream circuit changes (a button was pressed and a motor is now being driven), and the downstream circuit now looks like a 10-Ohm load, to keep the constant 10mA current your Series-Regulator will automatically set the transistor to act like a 490-Ohm resistor (keeping the 500-ohm system, so 10mA remains constant).
2. Shunt Regulator -- The transistor is treated as an adjustable resistor "in parallel" with the rest of the circuit. This "diverts" excess energy to ground, causing the rest of the circuit to effectively function within its specifications. Ex: If "downstream", you sense a 100-Ohm load and you have a target-current of 10mA and your source current is 50mA, you set the transistor so that it is equivalent to 25-Ohms. This shunts 40mA to ground, and the remaining 10mA goes to the 100-Ohm load.
But if the downstream circuit changes (a button was pressed and a motor is now driven), and the downstream circuit now looks like a 10-Ohm load... to keep the constant 10mA current your Shunt-regulator will automatically set the transistor to act like a 2.5-Ohm load. This shunts 40mA to ground and the remaining 10mA goes to the 100-Ohm load.
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Traditionally, series and shunt regulators sense voltage (not current), but its not very difficult to turn a voltage-regulator into a current-regulator instead.
Series regulators are your typical 7905 or whatever. They are more efficient (as you can tell by their obvious operation) and simpler to use.
Shunt regulators are traditionally Zener Diodes, or other circuits that are based "like" a Zener Diode. They can generate constant voltage offsets reliably (ex: if you have a 9V line from a series regulator, and you need a 7V reference, you can use a shunt-regulator to very accurately create -2V).
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As you can see, its all "pulling tricks".
Of course, the switching regulator (Ex: MC34063. Don't use, this is an old chip lol. But maybe TI's Simple Switcher series, or similar), truly "push" current thanks to an externally supplied inductor... and as a result lead to far superior efficiency specs.
Another "pushing" trick is a charge-pump. You can turn on capacitors in such a way that they double the voltage. That's the thing about "pushing", you need an ability to increase voltage until the "downstream" circuit acts the way you like.
Inductors (and capacitors, to a lesser extent) _can_ push. But its dangerous and somewhat difficult to design well. (Fortunately, we have pre-made modules like TI's Simple Switcher or Microchip's MCP1640, etc. etc. that do the job for us automatically... as well as pre-made power supplies).