Speaking for the benefit of all humanity, Lord Sri Krishna explained to Uddhava, his dearest companion, how guru is non-different from Himself:
ācāryam mām vijānīyān nāvamanyeta karhicit na martya buddhyāsüyeta sarva deva mayo guruh
“O Uddhava, you should consider the acharya to be my dearest embodiment, indeed my very self. Thus never disrespect him by being envious of him or thinking him to be an ordinary man, for he is the sum total of all the demigods.”(Srimad Bhagavatam 11:17:27)
Following these words of the Lord, Krishna Das Kaviraj wrote:
yadyapi āmāra guru caitanyera dāsa tathāpi janiye ami tānhāra prakāśaguru krsna-rūpa hana śāstrera pramāne guru-rūpe kṛṣṇa kṛpā karena bhakta-gane
Although my spiritual master calls himself a servant of Lord Chaitanya, I know him as a direct manifestation of the Lord.
According to the scriptures, the spiritual master is a form of Krishna. Krishna takes the form of the guru to bestow His mercy on the devotees.” (Chaitanya Charitamrita 1:1:44-45) Krishna is the supreme object of love and the root of all existence. In order to remind the fallen jivas of their forgotten nature, He takes the form of the spiritual master. He initiates them by giving mantras and teaches them how to engage in the Lord’s bhajan. This is how He shows His mercy. Our most worshipable Srila Prabhupada comments on the above verses in his Anubhāsya as follows: Even though the spiritual master is factually the servant of Lord Krishna Chaitanya, the disciple should understand that from the transcendental point of view, he is a special manifestation of the Lord. However, this does not mean that the guru has given up his relationship with the Lord as servant to master, or that he is in every way identical with Krishna and can take his role in nitya-līlā.No acharya on the devotional path would ever say that there is absolutely no difference between himself and the Supreme Lord; rather the he teaches the principle of inconceivable oneness and difference.
Raghunath Das Goswami instructed his mind to “think of the spiritual master as the beloved of Mukunda” (mukunda-presthatve guruvaram).In Bhakti-sandarbha (213), Jiva Goswami states:
śuddha-bhaktāḥ śrī-guroh śrī-śivasya ca bhagavatā saha abheda-drstim tat-priyatamatvenaiva manyante
Pure devotees consider the spiritual master and lord Shiva to be one with the Lord in that they are most dear to Krishna, and not for any other reason.
Srila Visvanath Chakravarti Thakur follows the same line of thought when he sings:
sākṣād-dharitvena samasta-śāstrair uktas tathā bhavyata eva sadbhih kintu prabhor yaḥ priya eva tasya vande guroh śrī-caraņāravindam
All the revealed scriptures and saintly persons state that the guru is Krishna Himself. However, the guru is glorified as the Lord’s dear-most servant because he is authorized to engage in His most intimate service. I consider myself to be the servant of my spiritual master and offer my respectful obeisance unto his lotus feet. (Gurvastakam, 7)
With this understanding, every Gaudiya Vaishnava meditates on his spiritual master as being tadiya – one who is totally given over to the Lord. Thus the ancient manuals of instruction for bhajan that are followed in the Vaishnava world, as well as the pure devotional songs of the Mahajans, all describe the spiritual master as either the manifestation of Nityananda Prabhu or a handmaiden to the Divine Couple.
Chaitanya Vani, 29.3-4. pp. 49-51 and 74-76.; HDG Srila Bhakti Promode Puri Goswami Thakur