Which type of proteins associate with the lipid bilayer but do not span the membrane?

Peripheral proteins are indeed the type of proteins that associate with the lipid bilayer but do not span the membrane. They are typically found on the cytoplasmic or extracellular surfaces of the membrane, interacting with integral proteins or phospholipids. Their attachment to the membrane is often mediated by non-covalent interactions, such as hydrogen bonding or ionic interactions, allowing them to perform various functions such as signaling, maintaining cell shape, and facilitating cellular communication.

In contrast, integral proteins, which include transmembrane proteins, extend across the membrane and often interact with both the internal and external environments of the cell. Transmembrane proteins are a subtype of integral proteins that specifically pass through the membrane multiple times. Membrane proteins is a broader term that can refer to both integral and peripheral proteins, making it less specific in this context. Therefore, peripheral proteins are correctly identified as those that associate with the membrane without spanning it.