Dear Malgosia,
if you peruse the LAStools group you should find a few prior posts that explain the difference between lasgrid and las2dem.
lasgrid simply puts an x/y grid over all the points and looks which points falls into which grid cell. It then applied to all points of a cell the desired operation: keep the maximum, keep the minimum, compute an average, or compute the stddev. The result is stored in the DEM. Grid cells that have no points falling into them remain empty rasters unless you specify '-fill 1' or '-fill 2' in which case a simple neighbor averaging is done to fill empty rasters from the 1-ring (or if needed the 2-ring) of filled neighbors.
http://lastools.org/download/lasgrid_README.txtlas2dem computes a triangulation (a TIN) of all the points. It then puts an x/y grid over the TIN and samples the elevation of the TIN triangles at the grid cell. Because the triangles interpolate across voids in the point distribution this should be your tool of choice when you create a DTM (i.e. you will be using only the ground points). if the triangles get too large they do not get "rasterized". this is controlled by the '-kill 500' switch that specifies the edge length at which triangles should get killed. the default is 100.
http://lastools.org/download/las2dem_README.txtCheers,
Martin @rapidlasso