The Gram stain is ineffective for acid-fast bacteria due to their mycolic acid-rich cell walls, which resist decolorization. In the Gram staining process, bacteria are differentiated based on their cell wall composition, with Gram-positive bacteria retaining the violet stain, whereas Gram-negative bacteria turn pink after the application of a secondary stain. Acid-fast bacteria may appear similar to Gram-positive bacteria but do not lose color because of their unique cell wall characteristics.