1st mistake - for a class 'D' CTR (most regional airports) it will only become a SVFR clearance if the vis is below 5km.
What you might be getting confused with is licence privileges which states that as a bare PPL you can't accept a SVFR clearance unless the in flight vis is 10km, or you're flying on a route specified as available (this normally means in the circuit, or following a published departure route).
As far as you're concerned - no difference in how it's handled from an ATC perspective (apart from the fact that we have to separate SVFR from IFR, but that's our problem, not yours). The main thing you have to think of is - can you accept the SVFR clearance? Unless you have an instrument or IMC rating on your licence the answer will probably be no. Whereas if the clearance is VFR then you can accept it quite happily.