Silkspan expands when wet, then dries to the same size it was before.  The one time I put it on dry no amount of tautening dope would tighten it.  Every time I've put it on damp it's dried to the perfect tautness.

Different brands may act differently -- my only experience is with Sig.  Doctor paper may act differently, too.

Tissue definitely shrinks.  It should only go on damp or wet if you're covering a compound curve.  For outdoor rubber powered planes I like to shrink it by wiping it down with a cotton ball that's been wetted with 70% isopropyl alcohol.  That makes for a nice even application of just the right amount of water when the alcohol flashes off.  For indoor rubber or really small outdoor planes you shrink the tissue on a frame, then cut it off, crumple it a bit, then put it on the plane.  Otherwise your plane will potato-chip as the tissue shrinks.

I think I'd only use tissue on 1/2-A planes, and then I may use it double-thickness.  If you go out and buy it, stick to Esaki -- all the other stuff I've bought recently has been crap.

Silkspan is made up of rotten silk threads. Not unlike expensive paper made from cloth, like our paper money.

Hmm.  Come to think of it, dollar bills might be less expensive than silkspan!  Too bad they come cut up into little rectangles.

If they're rubber powered, it's almost certain they're tissue. It should say on the box or in the directions.