Well, the Bible has been translated into Syriac, so we can simply compare the original Aramaic verses with the Syriac translation.
(I’m transliterating the Syriac into Hebrew script because it’s easier for me, it doesn’t affect anything)
Daniel 5:1 - בֵּלְשַׁאצַּר מַלְכָּא, עֲבַד לְחֶם רַב, לְרַבְרְבָנוֹהִי, אֲלַף; וְלָקֳבֵל אַלְפָּא, חַמְרָא שָׁתֵה
Syriac Translation - בלטשצר מלכא עבד לחמא רבא לאלף רורבנוהי ולוקבל אלפא חמרא שתא הוא
One of the big differences is that Biblical Aramaic the nouns and adjectives appear without an alef many times, while you rarely see that in later forms of Aramaic, where ending a noun and adjective with an alef is the norm.
Spelling is different, syntax is different and the pronunciation seems to have been very different between the two, but it’s hard to present it here.
Daniel 3:5 shows bigger differences between the texts.
Original: עָנֵה מַלְכָּא וְאָמַר לְכַשְׂדָּאֵי, מִלְּתָה מִנִּי אַזְדָּא: הֵן לָא תְהוֹדְעוּנַּנִי, חֶלְמָא וּפִשְׁרֵהּ, הַדָּמִין תִּתְעַבְדוּן, וּבָתֵּיכוֹן נְוָלִי יִתְּשָׂמוּן
Syriac translation: ענא מלכא ואמר לכלדיא: שרירא הי מלתא דאמרת, דאן לא תחוונני חלמא ופשרה, הדם תתפסקון, ובתיכון יתבזזון
Here the difference is mostly in vocabulary and idiom, with some obvious pronunciation differences like kaldaya instead of kasda’e.
Aramaic is the language of the Aramaeans, a Semitic people who originate from the areas that today are central and southern Syria. Through their importance as scribes and merchants, their language spread throughout the Fertile Crescent as an international lingua-franca and eventually becoming the native language of many other nations, including the Babylonians, Assyrians and Jews. The situation is comparable to the process that happened later with Arabic, which is today the majority language in the areas where Aramaic once was. It was used as a language of international communication between the Assyrians and the Egyptians, and was also widely used by the Achaemenid Persian Empire - Aramaic inscriptions have been found as far east as Pakistan.
Aramaic had and still has many different dialects and alphabets used to write it. Imperial Aramaic is the version that was used official by the ruling Empires in the Middle East. It wasn’t static though, and underwent changes over time, for example, under the Persian Empire Imperial Aramaic started using many Persian loanwords. Other versions of Aramaic are: Biblical Aramaic (close to Imperial), Jewish Babylonian Aramaic, Mandaean, various Neo-Aramaic dialects spoken today (Turoyo, Suret, Lishana Deni etc.) and Syriac.
Syriac is the dialect of Aramaic that was spoken in Edessa (today Şanlıurfa in southern Turkey) which was an important center of Christianity in the first centuries AD. Because of the importance of the city, a lot of important Christian literature was written in this dialect, including translations of the Bible into Syriac, and so this dialect became the liturgical language of Aramaic-speaking Christians, creating what is known as Syriac Christianity
, which today includes Catholic, Eastern Orthodox and Eastern churches. Syriac developed to have two main standards in terms of alphabet and pronunciation, Eastern and Western, though there could be some more variation.