Re: Are proteins EMBEDDED WITHIN A SINGLE phospholipid layer called extrinsic?

You are correct that the classification of membrane proteins as integral
(intrinsic) and peripheral (extrinsic) can appear to be broad terms. 
Peripheral membrane proteins, or extrinsic proteins, do not interact with
the hydrophobic core of the phospholipid bilayer. Instead they are usually
bound to the membrane indirectly by interactions with integral membrane
proteins lipid bilayer or to integral proteins by a combination of
hydrophobic, electrostatic, and other non-covalent interactions.
Integral membrane proteins are classified as intrinsic since their domains
are often embedded in the phospholipid bilayer.  A majority of integral
membrane proteins transverse the entire phospholipid bilayer.  These
transmembrane proteins contain one or more membrane-spanning domains
extending into the aqueous medium on each side of the bilayer. 

There are also integral proteins are anchored to one of the membrane
leaflets through specific interactions with the polar heads.  However, they
are considered extrinsic in that they can be removed without using
detergents to disrupt the lipid bilayer completely, but they are intrinsic
in that they are permanent parts of the membrane and retain some tightly
bound lipids when removed. An extrinsic membrane protein is removed from
the membrane by relatively mild means such as disrupting the ionic contacts
with salt.  Whereas, intrinsic membrane proteins are removed from bilayers
only by more severe treatment. This is defined as some treatment which
solubilizes or partially solubilizes the membrane; either treatment with a
detergent or apolar solvent that will disrupt the structure of the bilayer
and remove intrinsic proteins.