In large scale cosmological structure, are filaments, walls, sheets and nodes different terms for the same things? As the question says - are these all essentially synonyms referring to the same phenomenon (described with different words depending on the specific superficial appearance)? Or do they convey a real distinction and refer to essentially different phenomenae?
 A: They are not quite the same things, but you are correctly picking up on them being somewhat loosely (i.e. subjectively) defined concepts.  In cosmological structure formation, you start with a nearly smooth fluid of matter (mostly dark) which is gravitationally *unstable(.  The first mode of collapse is from the smooth 3D structure into 2D "sheets" (planar over-densities).  Once these sheets form, they are also gravitationally unstable, and the next mode of collapse is within the 2D sheets to form 1D "filaments".  Finally the filaments both start to collapse into 0D "nodes", and flow into places where numerous filaments come together--- these locations are usually the site of galaxy-cluster formation.
We are used to things undergoing spherical gravitational collapse, but in a fairly uniform medium (as seen in cosmology, but also in star formation from large molecular clouds) there isn't the same symmetry.  One way to think about it is: if you imagine perturbations on all shapes and scales (as is the case for many astrophysical random processes), then perturbations with planar symmetetry (like sheets) will have gravitational forces that are relatively constant with distance, i.e.  $F(r) \propto k$.  Perturbations with cylindrical symmetry (like filaments) have forces like $F(r) \propto k/r$, and finally spherical perturbations (like nodes) have standard $F(r) \propto k/r^2$.  Thus the order of instability tends to go something like [sheet $>$ filament $>$ node], which is the general order of their collapse (for a fixed length-scale).
Sheets, filaments and nodes are terms usually used to describe underlying structure observed in cosmological simulations or inferred from observations.  Still, nodes and filaments can easily be picked out of large-scale structure maps like the one attached*.  The highest density (orange) points are nodes, and the stringy, strands (green-yellow) are filaments.  Sheets are mostly observed at very high redshifts (early universe) in simulations.
"Walls" and "Voids" are more often used to describe features observed directly.  For example, a 'wall' might be like the giant, orange, line-like clump in the upper center.  The 'wall' description is usually used for images like this, where you are looking at a projection (no height information), but somewhat assuming that this 'wall' probably extends in/out of the page somewhat.  If, in 3D you saw that this structure was
actually more of a line, then 'wall' would be less applicable... these are loose terms.
A 'void' is like the empty black region just below 'the wall', in the attached figure.  If seems to have (and implies) a three-dimensionality to it.
*This image shows large scale structure as traced by galaxies and AGN (quasars) viewed by SDSS.

