Hindi-Urdu, also referred to as Hindustani, is the classic case of a digraphia, so much so that there has been a long-standing controversy over whether they are one language or two. Their colloquial spoken forms are nearly identical, but when written down, the one in the Devanāgarī script, the other in the Nastaʿlīq script, they have a very different look and "feel".
The question of whether Hindi-Urdu is one language or two may soon become passé, since — as the writer Ali Eteraz argues — the Urdu script is dying.
See "The Death of the Urdu Script", in which Eteraz asks, "Can Microsoft and Twitter save the dying Urdu nastaliq script from the hegemony of the Western alphabet and an overbearing Arab cousin?" Extensive comments and discussion on this article may be found here.
If, indeed, the Urdu script is dying out as Eteraz worries, it is ironic that it is not succumbing to or being swallowed up by Devanāgarī, but by the Arabic script known as Naskh or, worse yet, by Roman letters:
…[W]hen rendered on the web and on smartphones and the entire gamut of digital devices at our disposal, Urdu is getting depicted in naskh, an angular and rather stodgy script that comes from Arabic. And those that don’t like it can go write in Western letters.
This raises the question of the impact of the internet and of electronic information technology on the preservation and modification of scripts in general. Can all the scripts of the world be accommodated by digital media? To what extent do they have to be transformed in order to function with facility on the world wide web? Already we have seen handwriting in many languages deteriorate under the impact of widespread reliance on writing with electronic devices such as cell phones and computers. Perhaps now certain scripts that are much better suited for handwriting than for digital devices will have to make major adjustments in order to survive, while others may disappear altogether.
Language Log posts on Urdu language and script:
"Language in Pakistan", (12/28/2007)
"Camp language" (12/31/2007)
"Scripts, scriptures and scribes" (1/2/2008)
"A cricket writer enlightens us on the Urdu tense system" (8/31/2010)
"No word for rape" (11/20/2013)
"Is Cantonese a language, or a personification of the devil?" (2/9/2014) (see the first comment)
"Mutual intelligibility" (5/28/2014)