There is ample description of Sage Narayana and Brahman Narayana in Shreemad Bhagvat purana and others.
Let's see wht they tell us about your question.
Lord Narayanan as Supreme Brahman
Narayana is the Supreme God. From Vaishnavism point of view Supreme Para Brahman and is also known as Vishnu and Hari and is venerated as Purushottama or Supreme Purusha in Hinduism scriptures.
Narayana is the name of the Supreme God in his infinite all pervading form. He is the Supreme Purusha of Purusha Sukta. The Puranas present a seemingly divergent, but accurate description of Narayana (as an Enlightened Supreme Being).
The verses of the Narayana Sukta , a hymn in Yajurveda, states that Narayana pervades whatever is seen or heard in this universe from inside and outside alike.
नारायण: परं ब्रह्म तत्त्वं नारायणः परः।
nārāyaṇaḥ paraṁ brahma
tattvaṁ nārāyaṇaḥ paraḥ ।।
The Lord Narayana is the Supreme Absolute; Narayana is the Supreme Reality;
यच्च किञ्चिज्जगतसर्वं दृश्यते श्रूयतेSपि वा ।
तत्सर्वं व्याप्तं नारायण: स्थित: ।।
yacca kiñcijjagatsarvaṁ dṛśyate śrūyate'pi vā,
tatsarvaṁ vyāpya nārāyaṇaḥ sthitaḥ.
Whatever all this universe is, seen or heard of—pervading all this,
from inside and outside alike, stands supreme the Eternal Divine Being
Another important translation of Narayana is The One who rests on Water. The waters are called narah, [for] the waters are, indeed, produced by Nara [the first Being]; as they were his first residence [ayana], he is called Narayana.
Here is the relevant verse from Bhagvatam.
तास्ववात्सीत्स्वसृष्टासु सहस्रं परिवत्सरान् ।
तेन नारायणो नाम
यदापः पुरुषोद्भवाः ॥2.10.11॥
tāsv avātsīt sva-sṛṣṭāsu
yad āpaḥ puruṣodbhavāḥ
That Supreme Person is not impersonal and therefore is distinctively a
nara, or person. Therefore the transcendental water created from the
Supreme Nara is known as nara. And because He lies down on that water,
He is known as Narayana.SB 2.10.11
Here Narayana is Para Brahmam
यूयं द्विजाग्रया बत भूरिभागा ।
नारायणं देवमदेवमीश मजस्त्र भावा
yūyaḿ dvijāgryā bata bhūri-bhāgā yac chaśvad ātmany akhilātma-bhūtam
nārāyaṇaḿ devam adevam īśam ajasra-bhāvā bhajatāviveśya
O most eminent of brahmanas, you are all indeed extremely fortunate,
since you have already placed within your hearts Lord Sri Narayana —
the Personality of Godhead, the supreme controller and the ultimate
Soul of all existence — beyond whom there is no other god. You have
undeviating love for Him, and thus I request you to worship Him.SB
Here Shathapath Brahmana says Purusha Narayana carried out five days sacrifice and he became everything.
- Purusha Nârâyana desired, 'Would that I overpassed all beings! would that I alone were everything here (this universe)!' He beheld
this five-days’ sacrificial performance, the Purushamedha, and took
it , and performed offering therewith; and having performed offering
therewith, he overpassed all beings, and became everything here.
Now coming to Narayana Rishi. Sage Narayana is fourth incarnation of above supreme Purusha Narayana.Nara-Narayana are the twin sons of the wife of King Dharma.
धर्मस्य दक्षदुहितर्यजनिष्ट मुर्त्यां नारायणो नर ऋषि प्रवर: प्रशान्त:
नैष्कर्म्यलक्षणमुवाच चचार कर्म योSद्यापि चास्त
dharmasya dakṣa-duhitary ajaniṣṭa mūrtyāḿ nārāyaṇo nara
naiṣkarmya-lakṣaṇam uvāca cacāra
karma yo 'dyāpi cāsta ṛṣi-varya- niṣevitāńghriḥ
Nara-Narayana Ṛsi, who is perfectly peaceful and is the best of sages,
was born as the son of Dharma and his wife Murti, the daughter of
Daksa. Nara-Narayana Ṛsi taught the devotional service of the Lord, by
which material work ceases, and He Himself perfectly practiced this
knowledge. He is living even today, His lotus feet served by the
greatest of saintly persons.SB 11.4.6
bhārate 'pi varṣe bhagavān nara-nārāyaṇākhya
anugrahāyātmavatām anukampayā tapo 'vyakta-gatiś carati
The glories of the Supreme Personality of Godhead are inconceivable.
He has appeared in the form of Nara-Narayana in the land of
Bharata-varsa, at the place known as Badarikasrama, to favor His
devotees by teaching them religion, knowledge, renunciation, spiritual
power, sense control and freedom from false ego. He is advanced in the
opulence of spiritual assets, and He engages in executing austerity
until the end of this millennium. This is the process of
तुर्ये धर्मकलासर्गे नरनारायणावृषी ।
दुश्चरं तप: ॥1.3.9॥
akarod duścaraḿ tapaḥ
In the fourth incarnation, the Lord became Nara and Narayana, the twin
sons of the wife of King Dharma. Thus He undertook severe and
exemplary penances to control the senses.SB 1.3.9
Although the Names appear same ,Lord Narayana is supreme Brahman and unborn and Sage Narayana is incarnation of this supreme Brahman which is born out of womb. SageNarayana taught the devotional service of the Lord.