Question

What are the differences between the two major schools of Buddhism, i.e. Theravada and Mahayana ?

Answer 1

Other answers here provide useful history and details. I would suggest you disregard any sense of "lesser vehicle" and "greater vehicle," that was just ancient politics.

All the traditions are available today. So let's look at what each has to offer:

Therevada provides the most useful, detailed account of the Buddha's original teachings. If you want a sense of the Buddha's original ideas and the life of the ancient Buddhist sangha, start here. Some errors have crept it, but the data is solid. The careful logic and precision of meditation practice are profound.Mahayana gives us Zen, a living tradition of Awakened masters. None of them are perfect, but many are quite profound. It also gives a strong drive towards wisdom and compassion, and a lot of tools for getting unstuck on the meditation path. It also gives us a devotional path of Pure Land practice, which enriches the heart and life.Vajrayana has changed some core Buddhist ideas, such as adding reincarnation, which the Buddha was agnostic about. It offers an array of psychological practices to go with the core meditation practices taught by the Buddha and a strong heart of compassion.

Each tradition also has it's limitations. In brief:

The Therevadan tradition can give the idea that Buddha is far beyond us, and we cannot become Buddha in this lifetime. That is not what the historical Buddha taught. Also, some cultural elements, such as the idea that women are inferior, have crept in.The Mahayana can forget that the purpose of Buddhist life is the elimination of suffering. Sometimes, Enlightenment becomes a goal, rather than a step in the life process of becoming someone dedicated to the good of all at every moment, every breath.The Vajrayana can be boastful and competitive, with each of the four schools claiming to be the best way, and claiming overall superiority. It also tends to put mythology over history.

In the last, I don't mean to be critical. Religion is a human institution, and all human institutions end up full of erroneous ideas. Each tradition, at its heart, contains a well of Wisdom and Love. Used sensibly, with devotion and discretion, the traditions can add to our daily practice on the Way of meditation to the elimination of suffering.