The cell membrane contains channels and pumps that help move materials from one side to the other. What are these channels and pumps made of?

The plasma membrane of a cell form a selectively permeable barrier which regulates the flow of molecules, ions and other substances across it from the cell exterior to the cell interior and also from the cell interior to the cell exterior.
The lipid bilayer of the plasma membrane is hydrophobic in nature and so it is permeable to diffusion of gases and small non-polar molecules (with which it can form hydrophobic interaction or Van-der-Waals forces of interaction) across it.
However, the diffusion of small polar molecules and ions in restricted across the lipid bilayer. This is because these molecules form hydrogen bonds with water molecules and lipid molecules are incapable of forming hydrogen bonds and are water-hating in nature.
In order to facilitate the movement of these small polar molecules and ions across the plasma membrane there is a need of proteins which remain integrated in the plasma membrane and form a link between the cell interior and cell exterior.
These proteins are amphipathic in nature, that is, they are made up of both polar and non-polar amino acid residues.
The non-polar amino acids face towards the lipid molecules in the bilayer thereby forming hydrophobic interactions with the lipid molecules.
The polar amino acids face towards the channel or lumen across the lipid bilayer so that they can form hydrogen bonds with the polar molecules and ions which are transported across the plasma membrane.
These proteins either form Channels or Pumps.
Channel proteins form a continuous linkage in the form of a lumen between the cell interior and cell exterior across the lipid bilayer. However, they open this lumen only in response to the appropriate stimuli. They can remain open or closed, simultaneously, on either side of the membrane.
Pumps are made up of carrier proteins which do not form a continuous linkage but form a double-gated linkage in between the cell interior and cell exterior. They cannot remain simultaneously open on either side of the membrane. When they open in the cell interior, they remain closed in the cell exterior and when they open in the cell exterior they remain closed in the cell interior. Their opening and closing is also regulated by appropriate stimuli.