The grams stain is one of the most important stains in bacteriology/micro, etc. it pretty much divides bacteria into the 2 groups.
Gram positive is the purple/blueish dye, they retain the primary basic dye.
Gram negative happens when the species lose the primary dye and stain a pink/red.
The reaction of the bacteria- or colour to the gram stain is pretty much a reflection of the different chemical makeup of the cells of the two groups.
Gram positive obviously have a cell wall that contains fats/lipids talked about earlier.. (peptidoglycan)
Gram negative bacteria contains a layer of lipopolysaccharide which is absent in gram positive bacteria.
There are heaps of other ways to categorise bacteria.. This does not really group them into the pathogens/non-pathogens, it merely categorises the eubacteria into smaller groups.
-morphology/structural characteristics, growth, nutrition, biochemistry serology, genetics, ahh too many to type down- Are a few ways in which you can identify bacteria. The gram Staining is just one! (Of the broadest)
In order to find bacteria species and strains, you will have to use categorisation such as biochemistry, phage typing, and protein profiles....
*end rant*