Can you explain the difference between Krishna of Goloka and Krishna as an avatar of Vishnu in simpler terms?

 Disclaimer: this is an answer from the Vaishnava perspective.

Om Namo Bhagavate Vasudevaya!

There is a subtle difference.

Lord Krishna in the eternal Goloka is Bhagavan Svayam and Avatari (the source of all avataras).

Whereas Lord Krishna, who was on Earth, is a purna avatara of Lord Vishnu, a guna avatara of the Avatari Lord Krishna.

However, both are the same Supreme Person.

Explanation:

In Vaishnavism, Bhagavan Svayam resides in the eternal abode – the Param Padam.

tad viṣṇoḥ paramam padaṃ sadā paśyanti sūrayaḥ
divīva cakṣur ātatam

Translation:

“The wise ever contemplate that supreme station of Viṣṇu (the all-pervading one), as the eye ranges over the sky.” - Rig Veda 1.22.20

According to Panchratra philosophy, Bhagavan Svayam is ParaVasudeva (as recognised by Krishnavites) or Sriman Narayana (as recognised by Madhva and Sri Vaishnavas).

ParaVasudeva is recognised as Avatari because He is the source of all avataras, which includes the:

• Catur Vyuhas (Vasudeva, Sankarshana, Pradyumna, Aniruddha)
• Purusha avataras (Karanodakasayi/Maha Vishnu, Garbhodakasayi Vishnu, Kshirodakasayi Vishnu)
• Guna avataras (Brahma-Vishnu-Mahesha)
• Leela avataras (e.g. Rama, Krishna, Narasimha)
• Shaktyavesha avataras (e.g. Narada muni and Sanat-kumaras)
• Manvantara avataras (e.g. Hari and Yajna)
• Yuga avataras (i.e., incarnations of Satya, Treta, Dvarpara, and Kali yuga)

ete cāṁśa-kalāḥ puṁsaḥ
kṛṣṇas tu bhagavān svayam
indrāri-vyākulaṁ lokaṁ
mṛḍayanti yuge yuge

Translation:

“All of the above-mentioned incarnations are either plenary portions or portions of the plenary portions of the Lord, but Lord Śrī Kṛṣṇa is the original Personality of Godhead. All of them appear on planets whenever there is a disturbance created by the atheists. The Lord incarnates to protect the theists.” - Srimad Bhagavatam 1.3.28

ParaVasudeva is eternally residing in the Param Padam, He does not directly involve Himself with any work in the material realm whatsoever.

This is done by His expansions as the Purusha avatars, who are involved in the manifestation, maintenance, and dissolution of multiple universes simultaneously.

ādyo ’vatāraḥ puruṣaḥ parasya
kālaḥ svabhāvaḥ sad-asan-manaś ca
dravyaṁ vikāro guṇa indriyāṇi
virāṭ svarāṭ sthāsnu cariṣṇu bhūmnaḥ

Translation:

“Kāraṇārṇavaśāyī Viṣṇu is the first incarnation of the Supreme Lord, and He is the master of eternal time, space, cause and effects, mind, the elements, the material ego, the modes of nature, the senses, the universal form of the Lord, Garbhodakaśāyī Viṣṇu, and the sum total of all living beings, both moving and nonmoving.” - Srimad Bhagavatam 2.6.42

Relative to each universe, this act is carried out by the three guna avataras.

• Brahma (akara) - creates the universe as instructed to Him by the knowledge revealed to him by the Lord.
• Vishnu (ukara) - maintains the universe by residing in each atom of existence but also through incarnating in various leela-avataras.
• Mahesha (makara) - destroys the universe by His cosmic dance as Nataraja

“In order to handle creation, sustenance, and destruction the one and only Janaardhana takes the names of Brahma, Vishnu, and Maheswara.” - Vishnu Purana 1.2.6.11

Of these three, Lord Vishnu is seen as a purna avatara (complete incarnation of Bhagavan Svayam), whereas Lords Brahma and Shiva are seen more as shaktyavesha avataras (empowered incarnations) in this sense (though Lord Shiva holds special positions in some Vaishnava traditions – e.g., Gaudiyas and Ramanandis).

Hence, Lord Vishnu is completely nondifferent from Him and recognised as the same Supreme Person.

sṛjāmi tan-niyukto 'haṁ
haro harati tad-vaśaḥ
viśvaṁ puruṣa-rūpeṇa
paripāti tri-śakti-dhṛk

Translation:

“By His will, I [Lord Brahma] create, Lord Śiva destroys, and He Himself, in His eternal form as the Personality of Godhead, maintains everything. He is the powerful controller of these three energies.” - Srimad Bhagavatam 2.6.32

Lord Vishnu has many leela avataras, and of those, three are recognised as purna – Narasimha, Rama, and Krishna.

“Matsya, Kūrma, Varāha, Narasiṃha, Vāmana, Rāma, Paraśurāma, Kṛṣṇa, Buddha and Kalki are the ten Vibhavas (incarnations) of Brahman, the highest soul. The group of six qualities is said to exist in Nṛsiṃha, Rāma and Kṛṣṇa.” - Padma Purana, Uttara-Khanda 229.41–42

Lord Krishna here is the cowherd boy who descended to Earth and performed leelas to maintain dharma as an incarnation of Lord Vishnu.

This is the difference.

Lord Krishna of the Param Padam is eternal, existing in His original form, and does not leave this abode in any way.

He can simultaneously appear within the material universes without abandoning His transcendental abode.

Lord Krishna, who descended on Earth, remained on Earth temporarily in a form in this material realm and is also present in other different universes.

There are other Lord Krishnas as purna avataras of the various Lord Vishnus of the other universes.

But they are the same Purushottoma playing the leelas for our own benefit in different forms.

Hare Krishna