Hinduism, the word having its roots in Indus (the river), refers to the religion and philosophies that were prospering in the land around and beyond the river Indus. Hinduism originally was spread throughout the world (1), but at some later periods of time it has been practiced only in the Indian subcontinent. The discipline having no founder for itself and is in existence from the time undefined does not refer to itself as Hinduism. It was the people from outside who discovered this practice called it by this name Hinduism and now that has been generally referred to by this name only.
Originally the names that were used to refer to this discipline are vaidIka dharma (meaning discipline of vedas) and sanAtana dharma (meaning eternal discipline). If the religions practiced in the subcontinent are referred to as Hinduism it would mean a broad umbrella, which includes the Jainism, Buddhism and various other religions that took birth in this land and then spread to the other parts. These religions share many of the common roots with the sanAtana dharma. Hinduism being an open framework and these philosophies and customs are very closely associated with the main streams, it may not be wrong all together to call them so. However, as Hinduism is vaidika dharma - based on vedas, and since Jainism and Buddhism do not base their doctrines on vedas, in these sections generally Hinduism would mean the core Hindu discipline - based on vedas.
It is quite important to note the fact that it is a discipline and not a religion by the terms as defined for most other religions. As already said, it is actually, a framework where different religions and philosophies build on the core knowledge and grow.
To the Lord Who is already Eternal, let us hail, "Long Live".