Maybe a bit of history will help:
"Assyrian" and "Syrian" are not just differences in spelling, but the explanation is not quite that simple and conflicting usages have been sorely contested among 3 different Churches at various times - to the point of lawsuits in some instances.
In the simplest of terms:
- The Assyrian Apostolic Catholic Church, the Ancient Church of the East, and at least some within the Chaldean Catholic Church (all descended from a common Pre-Chalcedonian ecclesial ancestor) had long self-identified as "Assyrian". They did this as either a function of their Church affiliation, as an ethno-cultural identification, or both. They have also (formally or informally) utilized (or accepted) the usage "Assyrian Orthodox" at various points in their existence and the name has been used by others in reference to them in a way that suggested that it to be the Church's official name - which it never was.
- The Syriac or Syrian Orthodox Church (Oriental Orthodox) considered "Assyrian" to be an apt descriptor of their own ethno-cultural heritage and were also loath to use "Syrian" as an identifier in the US, because of concern that they would be confused with the Syrian (Antiochian) Orthodox of the Eastern Orthodox Communion. As a consequence, in the late 19th and early 20th century, those Syrian/Syriac Orthodox in the US came to favor "Assyrian Orthodox" as a descriptor.
- The Syrian (Antiochian) Orthodox of the Eastern Orthodox Communion (sometimes termed Roum (Roman) Orthodox or Melkite Orthodox in those days) never utilized "Assyrian" as a self-descriptor but were invested in the use of "Syrian".
- Meanwhile, just to add to the chaos, there was also a relatively short-lived phenomenon known as either "Assyrian Orthodox" or "Orthodox Assyrians". These were (Eastern Orthodox) ethnic Assyrians who came into communion with the Russian Orthodox and, ultimately, were assimilated into ROCOR.
In the late 19th and early 20th centuries, when only the Syriacs and Syrians (Antiochians) had any real presence in the US, issues were non-existent - the former regularly called themselves "Assyrians" and the latter termed themselves "Syrians". When faithful of the Assyrian Apostolic Church of the East started to become a noticeable identity, competition began to arise among the various ecclesia for the right to naming conventions.
The Syriacs fairly commonly (and even officially, at times) styled themselves as "Assyrian Orthodox" until at least the 1950s. And, until 1999, one would still occasionally encounter its usage in the names of some of its parishes, e.g.
, St. Mary's Assyrian Orthodox Church in Worcester, MA, its second parish in the US. However, confusian with the pre-Chalcedonian Assyrians was taking its toll and the Syriac hierarchy wanted to get past that.
The change of the Worcester parish's name to St. Mary's Syrian Orthodox Church was the subject of much rancor
, resulted in the loss of some parishoners, and was finally effected only after the direct intervention of the Syriac Orthodox Patriarch, His Holiness Mor Ignatius Zakka I Iwas. This despite the fact that Mor Ignatius had already addressed the issue in an Encyclical
issued almost 20 years earlier.
I am fairly certain that the Assyrian Orthodox Church of the Virgin Mary in Paramus, NJ, successor to the first Syriac parish in America, is the only Syriac/Syrian Orthodox one in which the older styling is still extant. (The issue of "trustee" ownership has a part in this and has allowed that parish to effectively refuse to do His Holiness' bidding in regard to renaming.)
(It is still the practice of the Armenian Apostolic Church to refer to the Syrian Orthodox as "Assyrian Orthodox", for reasons that are unclear to me.)
Albeit the transition from "Assyrian" to "Syrian" was not effected easily, the right of the Syriacs to use "Syrian Orthodox", their chosen alternative to the abandoned usage of "Assyrian" was much more problematic. The Syrian Orthodox of the Eastern Orthodox Communion were not ready to give up their favored terminology without a fight.
Ultimately, the question of who could legitimately use the designation "Syrian Orthodox Church of Antioch" was the subject of a civil court case between the Syriac and Antiochian Churches. The Syriacs won and, from that point onward, the Syrian Orthodox had to be content with "Antiochian" as a substitute.
The Russian-affiliated Assyrian Orthodox, whom I included primarily to make clear the diverse uses, were not a factor in any of these various conflicts. They never had a real presence in the US. They had one church in Baghdad which one author reported as accepting RO "dogma", but neither its jurisdiction or liturgy, although at least some of them were, for a time, induced to abandon their own liturgical praxis and accept the Liturgy of Saint John Chrysostom in Syriac. See pages 11 and 12 of A History of the Chaldean Mass
A thesis done a few years ago at St. Vladimir's presents a nice summary of the history and the issues about the name, including the rationale that lay behind the Syriacs' original assumption of "Assyrian" as an identifier. See: Syriac Orthodox Church in North America
As to whether Assyrians, Chaldeans, ansd Syriacs are ethnically the same peoples, one can find a number of decidely different opinions on this - particularly among those who deem themselves Assyrian purists.