You can think of alignments as being of two varieties: Those that describe orientation, and those that describe direction of movement.
Orientation alignments are more common, and those include "facing" (eg "facing line of dance"), "backing" (eg "backing diagonal center"), and "pointing" (eg "pointing to wall").
Directional alignments are used to specify direction of travel. There isn't as strict a protocol for describing direction of travel as there is for orientation, but certain terms frequently used are "traveling" or "moving", and "down", "towards" and "along". So for example, if the movement is to be along the line of dance, you might see "moving down LOD" or "traveling along LOD". Sometimes the extra verbiage is dropped altogether, and you'll see, simply, "LOD".
There are two primary reasons why technique books will choose to describe a directional alignment: (1) When the direction of travel is different from the orientation of the body, and (2) when the orientation of the body is too complex and/or variable as to be pointless to attempt to document.
An example of #1 is promenade position, where you might be pointing towards DW, but traveling in a direction which is directly down LOD. In this case, the alignment might be described as "Along LOD, pointing DW", or possibly "Pointing DW, traveling down LOD".
An example of #2 is many of the figures in Tango, where the feet, body and head may all be oriented slightly differently, and all different from the direction of travel. In this case, you might see an alignment described as "toward DC", or even just "DC". In this case, you know that the movement is to be directed towards diagonal center, even if the body might be turned slightly more towards the center (or more complicated yet, it may begin on the LOD side of DC and end on the center side). This is why they might opt to simplify the description.
I hope this makes sense.
Regards,
Jonathan