Buddha is a Sanskrit word that means "awakened one." A Buddha is someone who has realized the enlightenment that ends the cycle of birth and death and which brings liberation from suffering.
Is the fat guy Buddha, or is the skinny guy who meditates Buddha? They are both Buddha, but different Buddhas. The fat, laughing Buddha emerged from Chinese folklore in the 10th century. He is called Pu-tai in China and Hotei in Japan, and is said to be an incarnation of the future Buddha, Maitreya.
The early Pali texts names six Buddhas who lived before the historical Buddha, and one who will come after, who is Maitreya. Theravada Buddhism teaches that there is only one Buddha per age, and the Buddha of our age is the historical Buddha, the person born Siddhartha Gautama in the 6th century BCE. (In Theravada Buddhism, other people who have realized enlightenment during this age are called Arhats.)
He is also called Gautama (or Gotama) Buddha and the Tathagata (which means "he who is thus gone"). Mahayana Buddhists sometimes call him Shakyamuni Buddha, which means "sage of the Shakya." The Shakya was the historical Buddha's clan. As a rule, when English-speaking Buddhists refer to the Buddha, they are talking about the historical Buddha.
So the Buddha pictured as meditating is the historical Buddha? Not always. Mahayana art and literature are populated by a number of other Buddhas.
How Many Buddhas?
How many do you need? Seriously, it's not a fixed number. In Mahayana, Buddha-nature is the true nature of all beings. In a sense, everyone is Buddha. In the Zen monastery where I first studied Buddhism, the monks often pointed to the Buddha on the altar and said, "That's you."
To complicate matters further, the Mahayana doctrine of the Trikaya says that each Buddha has three bodies. These are called the dharmakaya, sambogakaya and nirmanakaya. Very simply, dharmakaya is the body of absolute truth, sambogakaya is the body that experiences the bliss of enlightenment, and nirmanakaya is the body that manifests in the world.
In Mahayana literature, there is an elaborate schema of transcendent and earthly Buddhas that correspond to each other and represent different aspects of the teachings. You will stumble into them in the Mahayana sutras and other writings, so it's good to be aware of who they are. As a rule, however, it's not necessary to know and memorize all the transcendent and earthly Buddhas to practice Mahayana Buddhism.
One exception might be Amitabha, or Amida, who has a special place in the Mahayana school known as Pure Land. Veneration of Amitabha is central to Pure Land Buddhism. This Buddha, who symbolizes mercy and wisdom, is most often pictured seated in a lotus blossom.
All Buddhas Are One
The most important thing to understand about the Trikaya is that the countless Buddhas are, ultimately, one Buddha, and the three bodies are also our own body. A person who has intimately experienced the three bodies and realized the truth of these teachings is called a Buddha.