The five levels of cell organization are 1.) the cell itself, 2.) the tissue made up by the cells, 3.) the organ made up by the tissues, 4.) the body system the organ belongs to, and 5.) the entire organism. The heart is part of the cardiovascular system, and the lungs belong to the respiratory system. These two organs (and systems) are very closely linked, because both play an important role in gas exchange.
Most cells that make up lung tissue are epithelial cells, which secrete mucus; however, there are also structural cells and nerve cells present. If you specifically look at alveolar tissue, the main cell types are macrophages (immune cells) and pneumocytes (epithelial cells). Pneumocytes can be squamous or cuboidal. Gas exchange occurs across the alveolar membrane, as CO2 diffuses out of the bloodstream and O2 diffuses into it.
Meanwhile, the heart is composed of mostly cardiac muscle tissue. At the cellular level, this type of tissue is composed of smooth muscle cells, fibroblasts (connective tissue cells), and cardiomyocytes (cells that contract the heart).
In terms of organelles, most cells are fairly similar. They have a nucleus for storing genetic information, ribosomes (located on the endoplasmic reticulum) to produce proteins and a Golgi apparatus to package them, mitochondria to create ATP, and lysosomes to break down waste and toxins.
Not every cell type will have all of these organelles, depending on what its function is—for example, red blood cells lack a nucleus, because they need to be small enough to fit through capillaries and reach other cells in the body. However, for the most part, cells require these organelles so that they can function the way they are supposed to.