Thanks Richard and Lob for your replies. Just to clarify I got it right:

EU vs non EU is clear.

But I did not understand why the 'issuing canton' would create a problem if one wanted to change. I would think that since one falls under the quota of the new canton, they might not give a B permit as their quota might be used up. So if one changes from Zurich to Zug for example, Zug might not issue a B permit (quota used up or need to prove skills are special etc. again). Why would canton zurich create a problem?