Krishna is worshipped in two registers that sit oddly together, and the tradition has spent centuries deciding which is primary.
The first is the Gita Krishna: the charioteer at Kurukshetra who, when Arjuna refuses to fight his own kinsmen, delivers a discourse on duty, action without attachment to its fruit, and the paths of knowledge, works and devotion, and then reveals a universal form that Arjuna cannot bear to look at. This Krishna is a teacher and a revealer, addressed in awe. The Bhagavad Gita's dating is unsettled, with estimates running from the fifth century BC to the first or second century of the common era and clustering around the second and first centuries BC, and turning partly on whether it was original to the Mahabharata or inserted later.
The second is the Vrindavan Krishna: the child who steals butter and is tied to a mortar by his exasperated foster-mother, and the youth who plays the flute at night so that the cowherd women leave their houses and their husbands to dance with him. This Krishna is not addressed in awe at all. He is teased, scolded, longed for and quarrelled with, and the emotional vocabulary of the devotion to him is drawn from parental love, friendship and erotic longing rather than from reverence.
Gaudiya Vaishnavism, the tradition of Chaitanya in sixteenth-century Bengal, made the second register decisive and built a theology on it: Krishna is not an avatar of Vishnu but the source of whom Vishnu is an expansion, and Radha, absent from the Bhagavata Purana and arriving through later poetry, is his own pleasure-potency and the model of the devotee. The relationship is illicit, and the tradition insists on that, because a love that risks reputation is held to be worth more than one that does not.
Both registers are alive. The same person may recite the Gita in the morning and sing about the butter thief in the evening without feeling any strain.