Surfaced vs Rough
Rough cut lumber has a rougher texture and more open fibers. The measurements run closer to a full dimension (Full Sawn) than a surfaced material. The faces of the board/beam can have a standard or resawn finish and the resawn finish can be bandsawn or circle sawn.
Surfaced lumber has many variations but the more uniform grain and slightly less splintery surface will give a more uniform color when stained. The rough dimensional lumber is run through a plainer set at a specific size. This makes all surfaced material much closer to each other in size than rough lumber. But all dimensions after plaining will be ½” below its described (or nominal) size. Therefore, a 2x4 S4S, will actually measure 1-1/2x3-1/2. But if stacked like lagging surfaced material will fit tighter together as there is less variation down the board. That is not to say that a rough-cut material may not be just as tight, or that the S4S may not have defects excluding it. But that is where ‘grade’ comes in. Surfaced materials can be surfaced on one side (S1S) up to all 4 sides (S4S). On some boards, if the material is narrow it will need to be specified if it is the large face of the board that has been surfaced (S2S) or if it the edges that has been surfaced (S2E). Or, if a surfaced board is ripped in half, it could be S2S1E.