What is the difference between Radharani and Lakshmidevi?
Krishna is the source of all incarnations of God like Narayana and Vishnu, and Srimati Radharani is the source of all expansions of Krishna's divine energy, para prakriti, or pleasure potency. Laksmidevi, the goddess of fortune, is one of Srimati Radharani's many expansions that accompany the Lord in His many incarnations.
"The beloved consorts of Lord Krishna are of three kinds: the goddesses of fortune, the queens, and the milkmaids of Vraja, who are the foremost of all. These consorts all proceed from Radhika." (Chaitanya Charitamrita, Adi 4.74-75)
" “The transcendental goddess Srimati Radharani is the direct counterpart of Lord Sri Krishna. She is the central figure for all the goddesses of fortune. She possesses all the attractiveness to attract the all-attractive Personality of Godhead. She is the primeval internal potency of the Lord.”(Chaitanya Charitamrita, Adi 4.83)
"According to expert opinion, Laksmi, the goddess of fortune, is a subordinate expansion of Srimati Radharani. As Krishna has numerous expansions of vishnu-murtis, so His pleasure potency, Radharani, also has innumerable expansions of goddesses of fortune."
—Krishna Book, Ch. 47)