Does the HX act as a subcooler in a traditional system, except that a compressed 1st stage gas will cool the condensed 2nd stage?

I'm still kind of learning about basic stages here, so please correct (and forgive) my ignorance. From my knowledge so far, in a subcooler, the suction line gas will cool down the liquid line to give the system a little bit of a boost? Or are you using a 1st stage liquid that is separated to cool a 2nd stage liquid prior heading to the evaporator?