Biomembranes
These are structures that are found in cells. The best known biomembrane is the plasma membrane, that separates the cell from the exterior --- but many internal organelles of the cell have their own membranes. Lipids are considered to be their main structural ingredient. Typically, they are bilayer structures: amphiphilic aggregates in which the lipids expose their hydrophilic "heads" to the water, while shielding the hydrophobic "tails" in the interior.
Model membranes
The term "model membrane" has a twofold meaning. For theoreticians, it usually means a theoretical model of the actual microscopic system. For experimentalist, it means a simplified mixture in which only the main ingredients are employed (usually: water, one or several species of lipids, and salts).