What is the difference between peptidoglycan and murein?

There’s no difference between peptidoglycan and murein. Both terms refer to the same thing – a complex network of sugar polymer and amino acids that surround the cytoplasmic membrane in bacterial cells. Each molecule within the network is made up of two joined amino sugars - N-acetylglucosamine (NAG) and N-acetylmuramic acid (NAM). These molecules are alternated in long chains and cross-linked to one another by a tetrapeptide that extends off the NAM sugar unit.

The term ‘peptidoglycan’ is derived from the peptide (amino acid) and glycan (sugar) component of the molecule.

The term ‘murein’ or ‘mucopeptide’ is derived from the N-acetylmuramic acid (NAM) component of the molecule.