here's a good post from the Gibson forum on what a 339 is...
In the smaller semi-hollow and archtop Gibson's there are two main lines
The ES-339 and ES-359 are 'brothers' sharing the same construction methods with the only differences coming in detailing and appointments. These are built like the classic ES-335: a center block surrounded by pressed-ply tops backs and sides. The 339 has the simpler appointments: dot inlays on a rosewood fretboard, single-ply binding, decal headstock, nickel hardware, usually plainer top woods.
The 359 has the "uptown appointments" very similar to an LP Custom: ebony fingerboard with big block inlays, the split-parallelogram inlay on the headstock, inlaid logo, gold hardware and triple-ply binding around the rims.
Everything else (pickups, construction, size, etc) is the same.
The CS-336 and CS-356 are another set of brothers, but from a somewhat different family: they are the same size & shape as the 339/359 but have a completely different "archtop" construction. The back & sides are routed (oops: "tonally carved") out of a single slab of mahogany, leaving a centerblock that's integral with the back and sides. They're then capped with bookmatched maple slabs and then "carved" or dished much like an LP top. Gibson's launch site for these in 2002 said that the top slabs and the back slab had sort of puzzle-piece protrusions & slots that helped connect the top to the centerblock for increased "tone coupling" (or something like that).
The CS-336 has the same general appointments as the 339: rosewood fretboard, nickel hardware, single-ply binding.
The CS-356 has the LP Custom style appointments: ebony board, fancy headstock, triple-ply binding, gold hardware.
All four guitars use Classic '57 pickups, but the ES ones use a different wiring scheme. All four are the same size/shape (substantially smaller than a 335, not much bigger/wider than an LP) and similar weights (usually between about 6.8 and 7.8 lbs, very balanced but lighter than a typical LP and most 335s). Neck profiles vary in hand made guitar necks, but all four have been made with both "60s" and "50s" sized necks.
It is said that perhaps the 339/359 has an "airier" sound slightly more 335-ish, while the 336/356 is capable of both a warm neck position and bright bridge position with knob twiddling, perhaps leaning a little in the LP direction on the 335-LP continuum. But these are, imho, very subtle differences... and of course generalizations. Individual guitars vary in sound, but the general character of all four of these is very similar, imho. To me, it's a very versatile design, and they all can do anything from jazz to blues to rock with ease.
And... if Gibson ever puts the 336, 356 and 339 back on their website along with the specs, I won't have to type this up every 5-6 weeks.