Greek manuscripts were written in the Greek uncial script from approximately the 3rd century BCE through the 12th century CE, and Latin manuscripts were written in the Roman majuscule script from the 7th century BCE through the 4th century CE. But even after miniscule script began being used, 'catholic church' was still rarely capitalized in the literature initially, because it likely was not being used as a proper title but rather as a simple adjective. The first use of the combination ἡ καθολικὴ ἐκκλησία ("the Catholic Church") is in the exact reference cited in the question (Ignatius of Antioch's Epistle to the Smyrneans 8:2, written approximately 110 CE. Since capitalization is irrelevant in this time period, it is best to allow context to help us understand the intended meaning. According to the Catholic Encyclopedia:
The word catholic "was freely used by the earlier Christian writers
in what we may call its primitive and non-ecclesiastical sense. Thus
we meet such phrases as the "the catholic resurrection" (Justin
Martyr), "the catholic goodness of God" (Tertullian), "the four
catholic winds" (Irenaeus), where we should now speak of "the general
resurrection", "the absolute or universal goodness of God", "the four
principal winds", etc. The word seems in this usage to be opposed to
μερικός (partial) or ἴδιος (particular), and one familiar example of
this conception still survives in the ancient phrase "Catholic
Epistles" as applied to those of St. Peter, St. Jude, etc., which were
so called as being addressed not to particular local communities, but
to the Church at large.
This Catholic Encyclopedia entry goes on to point out:
Among the Greeks it was natural that while Catholic served as the
distinctive description of the one Church, the etymological
significance of the word was never quite lost sight of. Thus in the
"Catechetical Discourses" of St. Cyril of Jerusalem (c. 347) he
insists on the one hand (sect. 26): "And if ever thou art sojourning
in any city, inquire not simply where the Lord's house is--for the
sects of the profane also attempt to call their own dens, houses of
the Lord--nor merely where the church is, but where is the Catholic
Church. For this is the peculiar name of the holy body the mother of
us all." On the other hand when discussing the word Catholic, which
already appears in his form of the baptismal creed, St. Cyril remarks:
(sect. 23) "Now it [the Church] is called Catholic because it is
throughout the world, from one end of the earth to the other...."
There can be no doubt, however, that it was the struggle with the
Donatists which first drew out the full theological significance of
the epithet Catholic and passed it on to the schoolmen as an abiding
possession. When the Donatists claimed to represent the one true
Church of Christ, and formulated certain marks of the Church, which
they professed to find in their own body, it could not fail to strike
their orthodox opponents that the title Catholic, by which the Church
of Christ was universally known, afforded a far surer test, and that
this was wholly inapplicable to a sect which was confined to one small
corner of the world. The Donatists, unlike all previous heretics, had
not gone wrong upon any Christological question. It was their
conception of Church discipline and organization which was faulty.
Hence, in refuting them, a more or less definite theory of the Church
and its marks was gradually evolved by St. Optatus (c. 370) and St.
Augustine (c. 400). These doctors particularly insisted upon the note
of Catholicity, and they pointed out that both the Old and the New
Testament represented the Church as spread over all the earth. (See
Turmel, "Histoire de la theologie positive, 1904, I, 162-166, with
references there given.) Moreover, St. Augustine insists upon the
consensus of Christians in the use of the name Catholic. "Whether they
wish or no", he says, "heretics have to call the Catholic Church
Catholic" ("De vera religione", xii). "Although all heretics wish to
be styled Catholic, yet if any one ask where is the Catholic place of
worship none of them would venture to point out his own conventicle"
(Contra Epistolam quam vocant Fundamenti, iv). Of later exponents of
this same thesis the most famous Vincent of Lerins (c. 434). His canon
of Catholicity is "That which has been believed everywhere, always,
and by all." "This", he adds, "is what is truly and properly Catholic"
(Commonitorium, I, ii).
I highly recommend you read the entire entry for more information. Of course later in history after the Eastern and Western church split, the bishop of Rome called the Western church the Roman Catholic Church, and the East opted to go with the title 'Orthodox.' It should be noted that the Greek adjective orthodox (ὀρθόδοξος) is dated to the late 3rd or early 4th century, and thus was in common use in the whole church prior to this split as well. It should also be pointed out that this distinction did not develop until much later in history (i.e. after the 11th century). Early on Eastern Christians were merely called "Greeks" and Western Christians "Romans." Phrases such as "the orthodox faith" and "the catholic church" were still applied to Christians both East and West (and still are in many ways).
To answer the question clearly, any speculation about the meaning of the word 'catholic' has nothing to do with capitalization. Only context can guide interpretation, in which case the Eastern Fathers tended to retain both uses: that of a title and as a simple adjective. It should be no surprise that Eastern Orthodox Christians today also retain both meanings, albeit using capitalization as a means of distinction.