In the surface of the skin are pores, tiny openings called a hair follicle. Deeper inside the pore, near the base of the follicle, there are sebaceous glands that produce sebum, a natural type of oil. That oil helps keep the skin flexible and protected.
Hair continues to grow through the surface, while oil or sebum oozes out the side and is spread around the area. Skin cells grow and die and are sloughed off through washing, rubbing or spontaneously. But that process can be interrupted when the pores close and when bacteria form inside them. The result is acne.
The white pimples that sometimes form are usually a combination of dead skin cells, white blood cells and bacteria. The trapped pus often creates an inflamed, red area around it. The term 'pus' is an adaptation of 'pustule', a type of acne that results when the follicle wall bursts and the white blood cells rush into the area as part of a healing process.
When the tiny bumps or spots appear black they're called blackheads, naturally enough. They're a non-inflamed form of acne that come from the material having poked through the surface. Their dark color isn't the result of contact with dirt on the skin. It's a combination of dead skin cells and sebum that have oxidized. Oxygen in the air causes a chemical reaction that turns them black.
Often, however, the material doesn't break the skin, but simply pushes it up, forming a small, white bump called whiteheads. One form are known as 'milia'. Normally dead skin cells will get washed off or simply fall off the surface. But they can get trapped underneath the surface. This type of acne is common among infants, but can affect people at any age.
All these variations go by a general medical term called 'comedones', and whether that formation is open or closed is part of the clinical difference between them.
As the acne develops it can variously form what are called papules, nodules or cysts. A papule forms when the walls holding the hair follicle burst near the surface. They're small and don't contain pus. A nodule is a hardened lump under the skin, resulting from a break at the base of the follicle. A cyst is a larger, reddened bump. They're soft, but can be very painful.