Because there are many different tissue types that make up both the heart and lungs, we will focus on only one type for each.
The heart is made up of a specialized type of tissue called cardiac muscle. At the organelle level, cardiac muscle cells (cardiomyocytes) have specialized connective regions called intercalated disks. These structures allow for the quick transfer of Na+, K+, and Ca2+ ions between cells so that action potential propagation (and thus cardiac muscle contraction) can be streamlined. Working together, these cells form the special muscle tissue of the heart, called cardiac muscle. Cardiac muscle lines all of the major valves of the heart so that blood can be pumped through regularly and with rhythmic, uninterrupted contraction. The cardiac muscle tissue combines with others, such as the valves, arteries, and specialized connective tissue, to make the heart proper. Finally, the heart is a part of the larger circulatory system.
In the lungs, one specialized cell type is the simple squamous cell. The structure of the cell—flat and extremely thin—permits the creation of spaces between the borders of individual cells for small molecules to pass through. These cells make up a part of one of the tissues of the lungs: the alveoli. Because they are made up of such a thin lining of simple squamous cells, the alveoli in the lungs are able to efficiently transfer O₂ to the adjacent capillaries and receive CO₂ in return. The alveoli, working in conjunction with other tissues, such as the capillaries, bronchioles, and connective tissue, make up the organ known as the lungs. Finally, the lungs themselves are part of the larger respiratory system.