Most of us swab the bore between shots to get better consistancy when using black powder (BP) or one of the substitutes. Some of the guys using Blackhorn 209 do not swab and claim it isn't necessary.
As for the swabbing, some use a solvent like T-17, others use Windex or alcohol and still others simply use a spit patch.
I shoot mostly BP or Pyrodex so what I do is after I load my rifle, I put a patch between my cheek and gum. Then after I fire, I remove the patch and swab the bore using both sides of the patch, then reload. I don't bother running a dry patch down the bore as I am going to shoot again immediately. And besides, the patch isn't really wet, just sort of damp.
If I notice the bore is getting really fouled or I am shooting a lot, I will swab with a few patches of windex/alcohol 50/50 mixture.