Gram-Positive and Gram-Negative Bacteria

Based on their cell wall structure, bacteria are either gram-positive or gram-negative as result of the gram stain (animation). "Negative" here meaning the initial crystal violet dye has not been retained so the lighter colored counter stain is more apparent.

Comparisons, Layers of the cell envelope, in order: (Image search)
Gram-Positive

1. Extracellular.
2. Thick cell wall, allowing more cross-link of amino acid side chains. 
• Presence of teichoic acid - a polysaccharide that can be used to identify gram-positive bacteria.
3. Plasma membrane. 
• No endotoxin or porin channel in plasma membrane.  
4. Intracellular.

Gram-Negative 

1. Extracellular. 
2. Outer plasma membrane. 
• Porin channels help the passage of nutrients. 
• Outermost lipid bilayer has lipopolysaccharide (LPS) instead of phospholipid.
• LPS contains an endotoxin called lipid A. Lysed gram-negative cells release lipid A into circulation, causing fever, diarrhea and septic shock.
3. Periplasmic space / Murein lipoprotein, which binds the outer membrane to the cell wall layer.
4. Thin cell wall / Periplasmic space. 
• No teichoic acid in cell wall. 
5. Inner plasma membrane.
6. Intracellular.

A thought on gram staining
Crystal violet and iodine are small enough to pass through cell membrane or cell wall. The subsequent complexes they make in the cell envelope is large, however still passable through porins. Alcohol strips away the outer membrane of gram-negative cells, allowing the complexes to leave past the lipid membrane.

LPS by Mike Jones

Gram-negative species are more dangerous
The outer LPS-containing membrane blocks antibiotics and chemicals from attacking the cell wall. This makes the bacterium resistant to lysosome and penicillin. The presence of endotoxin makes gram-negative bacteria more pathogenic than gram-positive bacteria.

Lipopolysaccharides (LPS)
0-antigen is a side chain specific to different organisms - think O for Outer. Lipid A is a disaccharide with fatty acid tails.

Transpeptidase 
An enzyme that cross-links the bacterial cell wall side chains.