No. It is a staining on the cell itself.

Gram staining was devised by Hans Christian Gram of Denmark in the 1800s. (1853-1938)

Differential staining is the procedure that are used to distinguish organism based on their staining properties. Use of gram stain divide bacteria into two classes - gram positive which retain crystal violet stain purple colour, gram negative which lose their crystal violet and give pink colour. By this method we can differentiate two different types of bacteria having different cell wall composition that is the reason gram staining used widely as differential staining

Differential staining is the procedure that are used to distinguish organism based on their staining properties. Use of gram stain divide bacteria into two classes - gram positive which retain crystal violet stain purple colour, gram negative which lose their crystal violet and give pink colour. By this method we can differentiate two different types of bacteria having different cell wall composition that is the reason gram staining used widely as differential staining

It tells the microbiologist/clinician facts about the cell wall construction of the bacterium. This then indicates which antibiotics to prescribe if you are trying to get rid of a bacterial infection.