Your getting confused between SPIC type ratings and licenses.
The CPL no matter how you did your training will not be good enough to be a Captain on a JAR25 multicrewed aircraft. You need an ATPL.
The upgrade process is same for all flavours of CPL you have experence requirments and then hoop jumping of a test etc. Different countrys do it in different ways.
Now if you have a SPIC type rating which limits you to a RHS again the country for your license dictates what you need to do. It may only be a LPC in the LHS or it may be a bit more involved depending on the orginal type rating.