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For the carboxylic acid-derived examples here, an acyl group is the group remaining after formal removal of $\mathrm{OH}$ from $\mathrm{R}-\mathrm{C}(=\mathrm{O})-\mathrm{OH}$. It includes the oxygen at the end of the fatty acid-derived chain, so it is more than just a hydrocarbon region. See IUPAC class names: carboxylic acids and derivatives.

The carboxylic acid-derived ester linkages in a triglyceride or typical glycerophospholipid have the form $\mathrm{R}-\mathrm{C}(=\mathrm{O})-\mathrm{O}-{\mathrm{R}}^{\prime }$. Here the acyl group is attached through oxygen to the glycerol-derived part. See IUPAC Blue Book, P-65.6: esters.

Glycerophospholipids are phospholipids built on a glycerol-phosphate scaffold. The illustrated two-acyl group form is common, but the subclass also includes other substitutions and one-chain derivatives. See IUPAC–IUB lipid nomenclature, Lip-2.2 and Lip-2.6.

Lipids are a chemically diverse family of chemical substances, conventionally associated with biological origin and solubility in nonpolar solvents. They include triglycerides, phospholipids, and cholesterol. The name does not specify one molecular formula, one repeating monomer, or one kind of polymer. Some lipids have both hydrophilic and hydrophobic regions rather than being uniformly nonpolar. See IUPAC Gold Book: lipids.

Structure explains the different jobs. A triglyceride has three fatty acid-derived acyl groups attached to glycerol and serves as an energy store. A typical glycerophospholipid instead combines two such chains with a phosphate-containing head, making it an amphiphile suited to a lipid bilayer. Cholesterol has a different structure and also contributes to cell membrane properties. Thus a lipid is a chemical building material, while a lipid bilayer is an organization of many molecules. See Clark, Douglas and Choi, Biology 2e, 3.3: lipid structures and functions.

Phospholipids are lipids containing a phosphate group as part of their structure linked by covalent bonds. The familiar membrane-forming phospholipids are amphiphilic: a hydrophilic head region with chemical polarity coexists with a hydrophobic, largely nonpolar hydrocarbon region. These descriptions refer to different parts of the same molecule, not to two separate substances. See IUPAC Gold Book: phospholipids and IUPAC Gold Book: amphiphilic.

A typical two-chain glycerophospholipid provides a useful example: a glycerol scaffold carries two fatty acid-derived acyl groups through ester linkages, plus a phosphate-containing head region. Phosphatidylcholine is one example. This scaffold describes an important subclass, rather than all phospholipids: sphingomyelin has a different backbone, and even glycerophospholipids need not all have two acyl groups. See IUPAC–IUB, Nomenclature of Lipids (1976), Lip-1.5 and Lip-2.1–2.6.

Polar does not mean negatively charged overall. At near-neutral pH, phosphatidylcholine is zwitterionic: its phosphate region carries negative electric charge and its choline region positive electric charge, with zero net electric charge for the molecule. Counting those opposite charges gives $(-1)+(+1)=0$; it does not remove their local interactions with water. See Lodish et al., Molecular Cell Biology: membrane lipids.

In a lipid bilayer, two membrane leaflets orient their hydrophilic heads toward the water on either side and their hydrophobic chains toward the shared interior. The hydrophobic effect helps explain this organization through the free energy of the water and lipids together. It is not a special repulsive chemical bond between chains and water. Which organization is favored also depends on molecular geometry, temperature, concentration, and the surrounding chemical solution; a phospholipid label alone does not guarantee a lipid bilayer. See Alberts et al., Molecular Biology of the Cell: the lipid bilayer.

This organization supplies a flexible barrier for compartments. A fluid lipid bilayer allows lipids to undergo diffusion within each membrane leaflet; barrier function therefore coexists with motion of molecules, as in the fluid mosaic model. It is not completely impermeable: small nonpolar molecules such as molecular oxygen and carbon dioxide cross much more readily than ions. In a cell membrane, ion channels and other membrane transport proteins provide selective routes; the existing membrane transport article explains their driving forces. See Alberts et al.: principles of membrane transport.

In 1925, E. Gorter and F. Grendel extracted lipids from red blood cells and compared the surface area of a one-molecule-thick film on water with the estimated total surface area of the red blood cells. Their table gave ratios near two, supporting a two-layer covering; they also proposed heads facing the aqueous surroundings on both sides. The inference depends on recovering the relevant lipids, estimating the red blood cell surface area correctly, and comparing compatible packing in the film and the cell membrane. It was indirect evidence, not an image of the lipid bilayer. The paper itself notes possible losses during evaporation. See Gorter and Grendel, On Bimolecular Layers of Lipoids on the Chromocytes of the Blood, Journal of Experimental Medicine 41 (1925), 439–443.

A triglyceride contains glycerol joined to three fatty acid-derived acyl groups through ester linkages. Compare the three chains with the two-chain, phosphate-headed glycerophospholipid illustrated below. See Biology 2e: fats and oils.