Theravada
In the Buddhist countries of southern Asia, there never arose any serious differences on the fundamentals of Buddhism. All these countries - Sri Lanka, Cambodia, Laos, Burma, Thailand, have accepted the principles of the Theravada school and any differences there might be between the various schools is restricted to minor matters.

The earliest available teachings of the Buddha are to be found in Pali literature and belongs to the school of the Theravadins, who may be called the most orthodox school of Buddhism. This school admits the human characteristics of the Buddha, and is characterised by a psychological understanding of human nature; and emphasises a meditative approach to the transformation of consciousness. The teaching of the Buddha according to this school is very plain. He asks us to 'abstain from all kinds of evil, to accumulate all that is good and to purify our mind'. These can be accomplished by The Three Trainings: the development of ethical conduct, meditation and insight-wisdom.

The philosophy of this school is that all worldly phenomena are subject to three characteristics - they are impermanent and transient; unsatisfactory and that there is nothing in them which can be called one's own, nothing substantial, nothing permanent. All compounded things are made up of two elements - the non-material part and the material part. They are further described as consisting of nothing but five constituent groups, namely the material quality, and the four non-material qualities - sensations, perception, mental formatives and consciousness. When that perfected state of insight is reached, i.e. Nibbana, that person is a 'worthy person' an Arhat. The life of the Arhat is the ideal of the followers of this school, a life where all (future) birth is at an end, where the holy life is fully achieved, where all that has to be done has been done, and there is no more returning to the worldly life'.
Central Ohio Theravadan Groups

Mahayana
The Mahayana is more of an umbrella body for a great variety of schools, from the Tantra school (the secret teaching of Yoga) well represented in Tibet and Nepal to the Pure Land sect, whose essential teaching is that salvation can be attained only through absolute trust in the saving power of Amitabha, longing to be reborn in his paradise through his grace, which are found in China, Korea and Japan. Ch'an and Zen Buddhism, of China and Japan, are meditation schools.

It is generally accepted, that what we know today as the Mahayana arose from the Mahasanghikas sect who were the earliest seceders, and the forerunners of the Mahayana. They took up the cause of their new sect with zeal and enthusiasm and in a few decades grew remarkably in power and popularity. They adapted the existing monastic rules and thus revolutionised the Buddhist Order of Monks. Moreover, they made alterations in the arrangements and interpretation of the Sutra (Discourses) and the Vinaya (Rules) texts. And they rejected certain portions of the canon, which had been accepted in the First Council.

According to it, the Buddhas are lokottara (supramundane) and are connected only externally with the worldly life. This conception of the Buddha contributed much to the growth of the Mahayana philosophy. The ideal of the Mahayana school is that of the Bodhisattva, a person who delays his or her own enlightenment in order to compassionately assist all other beings and ultimately attains to the highest Bodhi.
Central Ohio Mahayan Groups

Vajrayana
This is the kind of Buddhism predominant in the Himalayan nations of Tibet, Nepal, Bhutan, and also Mongolia. It is known as Vajrayana because of the ritual use of the vajra, a symbol of imperishable diamond, of thunder and lightning. At the center of Tibetan Buddhism is the religious figure called the lama, Tibetan for "guru"," source of another of its names, Lamaism. Several major lineages of lamas developed, beginning in the ninth century with the Nyingma-pa. Two centuries later, Sarma-pa divided into the Sakya-pa and the Kagyu-pa. Three hundred years later, one of Tibet's revered lamas, Tsong-kha-pa, founded the reforming Gelug-pa.
Central Ohio Vajrayanan Groups

Source: Buddhanet.net