Many people conflate languages with writing systems, but the two are not the same. The mistake can be forgiven because several high-profile languages do indeed have unique writing systems: Arabic, Russian, and Chinese, for example.
However, the generality is readily revealed to fail when we note that English, most Western languages, and a few other languages all use the so-called Latin alphabet. This is in spite of the fact that the basic Latin alphabet is insufficient for precisely spelling words in most of these languages. All supplement the basic letters with accents, umlauts, hatchecks, cedillas, and other diacritics or letters to indicate pronunciation more precisely. Until computers took over typesetting, even English placed an umlaut over the second vowel in words like “cooperate” and “reelect” to indicate that it was to be preceded by a glottal stop. (Some writers chose to hyphenate these words to force the glottal stop: co-operate.) The early computer character sets made diacritics difficult or impossible, and these simple English usages faded away, but not before whole books, computer-generated, were published with diacritics added by hand.
The spread of the Latin alphabet has a sometimes positive, sometimes sordid history. When Ataturk came to power in Turkey, one of his modernizing reforms was to switch the writing system to the Latin alphabet, thus aligning the nation in a more Westerly direction. Turkish scholars had to fiddle with several letters in ways not seen anywhere else so that some unique sounds could be represented.
On the sordid side, when France colonized Viet Nam, the French imposed the Latin alphabet on their language. This was quite a feat, since Vietnamese is a tonal language, in which rising, falling, and constant tones are as significant as spelling. The result is that in some words a letter might be decorated with as many as five diacritics. This suited the French, as well as the Americans who later took over the plunder of Viet Nam, because the changes made Vietnamese easier to learn.
When Islam conquered Iran, the Iranians were able to keep their language (Farsi, an Indo-European language unrelated to Arabic), but converted to the Arabic writing system.
The champion of alphabetic imperialism, however, is the former Soviet Union. By bringing into the empire several states and tribes along the southern region, they brought in scores of languages for which there was no direct spelling in the Russian alphabet (which already has 34 letters). The Soviets therefore added diacritics, modified letters, and even added new letters to accommodate the new sounds.
The Russian alphabet, called Cyrillic, is based largely on the Greek alphabet, and was designed by Cyril and Methodius, men affiliated with the Eastern Roman Empire and its Church. Today, countries that are predominately Eastern Orthodox use Cyrillic, while those that are Roman Catholic use the Latin alphabet. You might have expected the divide to be Slavic versus non-Slavic languages.
This results in a peculiar situation: Serbs and Croats speak the same language, Serbo-Croatian, but the the Serbs tend to be Eastern Orthodox, while the Croats are Roman Catholic; they use different alphabets! Since the spellings are quite parallel, it is possible to simply substitute letter for letter to “translate” from one to the other.
One final note: Although languages have evolved over the centuries, the older languages, along with their writing systems, tend to persist–beyond customary usage–in religious contexts. Thus, Sumerian survived along with its priests long after Sumer faded; Egyptian hieroglyphs and priests were still active in the 5th Century; the Etruscan language and priesthood outlived its founding culture*; the Russian Orthodox bible is in Old Russian Cyrillic**; and there are several more examples. This makes sense when you consider the inherent conservatism, often to the point of impracticality, of religions.
* The Etruscan priesthood, and spoken Etruscan, came to an end at the hands of the Roman authorities within hours of a failed prophecy.
** Correction: The language is Old Church Slavonic, which uses the earlier Cyrillic alphabet.