The term ‘Western Music’, in common parlance, is simply referred to as western because it is composed by trained musicians in the western hemisphere.
On the other hand, Indian Classical Music is something that is being written and produced by vernacular artists in many languages.
Although the roots of all the music across the globe are same, there are some broad differences between Western and Indian music.
When studying Indian classical, melody is primarily homophonic. A sequence of notes is used to create melodies in different Raagas. It is this basic framework that defines Indian classical music and makes it unique. Western classical music is an entirely polyphonic composition. The beauty of polyphonic compositions is that the textures are created using multiple voices. There is no single defining focus on melody, but a variation of voices that make it unique.
Western music is written using staff notations and there is no improvisation as such. The musicians follow the written music notations without any scope of improvisation. When learning Indian music, the teacher-student tradition gives each of them a scope to learn and improvise at the same time. There is no written work done while learning Indian music.
Both the forms of music use instruments along. In Indian classical music, however, instruments like Harmoniums and Tanpooras are only mere accompaniments with the primary focus on vocals only. Western music also uses instruments but in a manner that the composition carries a lot of weight. The structure is formed by the vocals itself but with is instrumentally-generated.
It is only a few differences here and there that differentiate Indian and Western music. But, the core of music and the way it influences the listeners to remain just the same.