Also: These days Sanskrit is either written with the Hindi script (Devanagari) or with the Latin one (IAST). Previously it was written in the script of the land (i.e. Sinhala, Tibetan, Thai, Khmer, ... ). But which one will the classic writers themselves (Vyasa, Manu, Patanjali, Shakyamuni, Nagarjuna, Prahevajra, ...) have used originally?
Put simply, things change. There used to be more writing systems in Europe, and there used to be fewer in Asia. Many of the writing systems of South Asia have a common shared ancestor. There are a huge number of social, political, religious or cultural reasons why writing systems may be replaced or may take alternate paths of development. This is still seen in recent history throughout the world.
You also have to remember that you're comparing two large areas with very different histories, geographies, social structures, etc etc etc. So it's not really reasonable to expect things to be the same between the two. The number of factors contributing to the differences in between two areas of the world are ultimately infinite. If they were totally consistent, that would be something needing some serious explanation, or at least investigation into a potential universal law that was being acted upon.
You may want to take a look at the Wikipedia article on the Brahmi script. Many of the modern writing systems in South Asia are descended from this, and with a high degree of visual similarity being retained in many cases. This is also one