In his purport to Srimad Bhagavatam 10.3.47, His Divine Grace A.C. Bhaktivedanta Swami Prabhupada describes this topic: "Srila Viswanath Chakravarti Thakur discusses that Krishna appeared simultaneously as the son of Devaki and as the son of Yasoda, along with the spiritual energy Yogamaya.
As the son of Devaki, He first appeared as Vishnu, and because Vasudev was not in the position of pure affection for Krishna, Vasudev worshipped his son as Lord Vishnu.
Yasoda, however, pleased her son Krishna without understanding His Godhood. This is the difference between Krishna as the son of Yasoda and as the son of Devaki. This is explained by Srila Viswanath Chakravarti Thakur on the authority of Hari-vamsa."