Since you are coming from a different CAD system, let's take a step back and describe how NX handles parts and assemblies. What you are describing sounds to me like basic NX assembly functionality.
Some CAD systems have multiple file types depending on the contents (model, drawing, assembly, etc); NX has only the one type (.prt files). An NX .prt file can be a model, drawing, or assembly. An assembly file contains links to the individual model files, but does not contain their geometry. In the model file you can create "reference sets" which define what geometry you want to see in the assembly; in this way you can filter out items such as datums, sketches, etc etc. When a part is added to an assembly, you can specify which reference set to use initially and of course, this can be changed later within the assembly. Every part will automatically have an 'entire part' and 'empty' reference set, and the out of the box (OOTB) default is to also create a reference set named "MODEL" that will automatically contain all the solid bodies (and optionally all the sheet bodies - zero thickness surfaces that do not enclose a volume). If the model file(s) and assembly file are open in the same session, any changes made to the models will automatically be shown in the assembly. A model file can be edited in the context of the assembly by making it the 'work part' (right click the component and choose 'make work part'). When a component is made the work part, all the defining geometry is loaded into memory (if it is not already) so that you may edit the defining features.
There are a few ways to create your assembly file, the most common work flows are called 'bottom up' and 'top down'. For illustration, let's say you are modeling a toy car. In the bottom up work flow, you would create a 'chassis.prt', 'wheel.prt', 'axle.prt', and 'body.prt'; then you would create a 'car.prt' and add the other files as components positioning them and/or constraining them as necessary. In the top down work flow, you would create the 'car.prt' and start modeling the other parts as solid bodies within this file. At such time in development that you decide you want a proper assembly, you can use the NX assembly function 'create component'. Using this function, you can select a solid body (or bodies) and NX will export the body and defining geometry to a new .prt file and add it as a component back to the car.prt file. Now you have all the defining geometry in its own file and a component (or link) to that geometry in the assembly file.
From your description it sounds like you started with the top down approach and are now looking for the way to create components. Make sure the 'assemblies' module is running then use the command finder to search for 'create component' to find the menu location. And of course, look up 'create component' in the help files for more information on its use.
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