The term in 1 Timothy 3:2 is ἐπίσκοπος (episkopos), whereas the term used in 1 Timothy 5:17 is πρεσβύτερος (presbyteros). The two offices continue to exist to the present day within the Greek Church the same names, with episkopos translated into English as "bishop" and presbyteros as "presbyter" or "priest".
I not sure one can infer anything conclusive about the roles and responsibilities at the time from a single verse. We do know that by the end of the 1st century there was a clearly defined clerical hierarchy consisting of episkopoi, presbyteroi, and a third office, diakonoi (deacons). All three are mentioned in the Praxapostolos of the New Testament, but there is not as clear a distinction in the roles of episkopoi and presbyteroi as emerged later. Ignatius of Antioch (35-108) wrote, for example,
Be ye subject to the bishop as to the Lord, for he watches for your
souls, as one that shall give account to God [viz. Hebrews 13:17].
Wherefore also, ye appear to me to live not after the manner of men,
but according to Jesus Christ, who died for us, in order that, by
believing in His death, ye may by baptism be made partakers of His
resurrection. It is therefore necessary, whatsoever things ye do, to
do nothing without the bishop. And be ye subject also to the
presbytery, as to the apostles of Jesus Christ, who is our hope, in
whom, if we live, we shall be found in Him. It behoves you also, in
every way, to please the deacons, who are [ministers] of the mysteries
of Christ Jesus; for they are not ministers of meat and drink, but
servants of the Church of God. They are bound, therefore, to avoid all
grounds of accusation [against them], as they would a burning fire.
Let them, then, prove themselves to be such.
Epistle to the Trallians, Chapter II
The Apostolic Canons (I and II) indicated that episkopoi were to be ordained by other episkopoi and that presbyteroi and diakonoi were to be ordained only by an episkopos.
A Russian Orthodox presbyter and theologian, Michael Pomazanski, provides a good overview, I think, of what the New Testament Scriptures tell us about the presbyteroi:
Presbyters (literally “elders”) were both in Apostolic times and in
all subsequent times — and are today [in the Eastern Orthodox Church]
— the second degree of the hierarchy. The Apostles Paul and Barnabas,
as the book of Acts relates, going through Lystra, Antioch, and
Iconium, ordained presbyters in each Church (Acts 14: 23). For the
resolution of the question about circumcision, an embassy was sent to
Jerusalem, to the Apostles and the presbyters at Jerusalem (Acts 15:
2). At the Council of the Apostles, the presbyters occupied a place
together with the Apostles (Acts 15: 6).
Further, the Apostle James instructs: Is any sick among you? Let him
call for the elders (presbyters) of the Church, and let them pray over
him, anointing him with oil in the name of the Lord (James 5: 14).
From the instruction of the Apostle James we see that (1) presbyters
perform the Church’s sacred rites, and (2) in the early Church there
could be several presbyters in each community, whereas only one bishop
was appointed for a city and the region around it.
In the twenty-first chapter of the book of Acts, it is related that
when the Apostle Paul returned to Jerusalem after his third Apostolic
journey and visited the Apostle James, all the presbyters came,
signifying that they made up a special Church rank. They repeated in
the hearing of Paul the decree of the Apostolic Council concerning the
noncircumcision of the pagans; but they asked him to perform the rite
of his own purification, so as to avoid the reproach that he had
renounced the name of Jew.
Orthodox Dogmatic Theology (3rd ed.), pp.253-254
Regarding the ambiguity between presbyteros and episkopos, he further writes:
In the Apostolic writings the two names of “bishop” and “presbyter”
are not always distinguished. Thus, according to the book of Acts the
Apostle Paul called to himself in Miletus the “presbyters of the
Church” from Ephesus (Acts 20: 17), and instructing them he said, Take
heed therefore unto yourselves, and to all the flock, over which the
Holy Spirit hath made you bishops (overseers), to feed the Church of
God, which He hath purchased with His own blood (Acts 20: 28).
However, from these and similar expressions one cannot conclude that
in the age of the Apostles the two ranks — bishop and presbyter — were
joined into one. This shows only that in the first century church
terminology was not yet as standardized as it became later, and the
word “bishop” was used in two meanings: sometimes in the special
meaning of the highest hierarchical degree, and sometimes in the usual
and general meaning of “overseer,” in accordance with the Greek usage
of that time.