I understand that we use an NMOS to form a constant current source. My question is, can we create a constant current sink using a similar approach with PMOS? Is constant current sink even a thing?
Constant Current Source is a term used in the
circuit theory (analysis/synthesis), as a construct to model real sources. It is meant as a source of
energy/
power, it sources energy, so
its opposite is load not
sink (from this point of view a load "sinks" energy). The constant current sink is not "a thing".
P.S.: The
ideal CCS gives, according to its name, a specified constant value of current into any arbitrary load, i.e. it does it under any circumstances (voltage across it is defined by the current and that load; so, for instance, CCS can give that current into a short circuit with zero voltage across the load, or if you disconnected the load, its voltage would go to infinity, trying to "push" the current through its disconnected terminals). Look at it as at a black box, at one component (here a source) of set of components used in the circuit theory. It does not distinguish source/sink orientation in terms of your question because here this does not give a sense. One pole of such a source is sourcing (taking into account the consensual current direction), the other is sinking current of the same value.
A real CCS always works as CCS only within specified range of conditions, outside them it does not (such a state is usually called saturation). In principle, it usually consists of a voltage source (a power supply) and a regulator that controls voltage across the intended load so that current flowing through it, measured as a voltage drop across a sensing resistor in series with the load, is constant. The output/power component of the regulator is often a BJT or MOSFET and we can speak about sourcing or sinking current in relation to their electrodes but not in relation to the whole current source (created by all the above mentioned components).
Btw., you've mentioned an NMOS to form a CCS, the drain of which acts as a sink not a source of current, as FvM also reminded.