I'll try to simplify this copy/monitor process for you.
The way this is supposed to work is on the RAC side of things, you are designing the model. At some point the structural consultant on RST needs the file so they can begin their calculations and what not. You send them the RAC file and they will use it as an underlay. They will link into their file and begin some general setup of the file. The set up includes acquiring shared coordinates. (Can be done from the tools menu.) This will help ensure that the two models are being developed on the same coordinates system and help ensure that the two models are in the same location as each other.
The next thing to be done is go into the Copy/Monitor command and do some setup in the copy/monitor settings. The first thing that should be done is to look at the grips option. Here it is a good idea to tell Revit to "reuse if levels match exactly."
What this will do is tell Revit if the levels are at the exact same elevation that it is to convert the default grids to match what the RAC model is using.
IE: RAC model = Level 1 @ 1500'-0"
RST model = TFE @ 100'-0" --COPY / Monitor-- becomes TOS @ 1500'-0" (level can be renamed after)
Then the structural consultant will continue through the copy/monitor settings and compare wall and floor systems between the two models. Here they can look at what type of wall are in the RAC model and decide what the wall will be in the RST model if/when the wall are copied.
The last settings they will look at are the setting for any columns that were placed in the RAC and again decide what type of column it will be if/when copied into the structural model.
Of course this can all be changed at any point after the copy / monitor process is finished for the session.
Once all the settings are set then they will begin the actual copy aspect of the command.
They will now go around the RAC model and select the levels and grids.
Then go through and pick walls and floors and columns to be copied into the RST file.
As soon as the copy is executed, Revit automatically does the monitor which will compare the two models to each other and notify the structural people of any changes made to objects that have been copied during this process only.
After they develop their model they will send it back to the Arch. team for them to start working with.
The process here is very similar but the Arch. team will not have to copy half as much and is generally frowned upon as it will drastically increase file size and decrease performance.
For the most part the Arch. team will do mostly monitoring so what will be done is execute the copy/monitor. Then you just select an object from the model to monitor and pick an element from the arch. model to monitor it to.
The important thing to remember here is you can only monitor an object if they have one two, meaning it is a two pick process.
After both teams have done the initial copy/monitor the teams continue swapping their files and as changes are made to both files, Revit will keep track of them and let both parties know what they are as well as options on how to handle the changes.
So, short version:
The Arch. and Struc. teams are developing and maintaining their own models, just using each other as a reference and underlay more or less.
The copy portion of the copy / monitor process is how the different consultants can get model elements into their file w/o having to recreate the information via the copy command. (CTRL C version)
The monitor portion of the copy / monitor is so Revit can observe and notify of the changes between the objects copied during the copy / monitor process.
An item to note, the only elements Revit will only allow on the Structural end of Copy/Monitor is:
Shared Levels and Grids
Along with this process is a whole series of best practices but I will spare you from them in here.
Hope this helps a little bit and didn't really confuse anyone.