Mobile or fixed pig trap design is something that each system needs to determine and no "norms" or standards IO am aware of will define this.
As MK3223 says, the key is frequency of operation and compatibility between different locations in terms of design pressure, ID, size, connection flanges.
The places where you tend to see mobile units are locations such as gathering systems where many lines at the same design, pressure size and ID are rarely if ever pigged and hence you can save CAPEX by reducing the number of pig traps.
I f you're operationally pigging anything more than once every year or two years, the extra operational and safety aspects normally out weigh any beneifit due to the time cost and safety issues in making and breaking containment on a regular basis.
If you want to connect to a live system then you still need isolation valves and they cost as much as the pig trap which is really just a bit of pipe and some nozzles and a fancy end closure.
I'm still not sure about your ID question, but I would always design a pig trap to the pipeline code, not PV or piping.
The ID of the throat is your issue and this should match exactly the connecting pipeline ID. If it is smaller then your pig either might get stuck on launch or not seal well in the actual pipeline. Too small an ID on receiver and you can rip the pig apart as it hits a square edge at the flanged connection or also get stuck.
Is that what you need to know?
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
