[Ask Mr. Religion]

I don't think the ESV equates receiving and believing. The ESV Study Bible entry for this verse is as follows:

John 1:12–13 Receive him implies not merely intellectual agreement with some facts about Jesus but also welcoming and submitting to him in a personal relationship. “Believed in” (Gk. pisteuō eis) implies personal trust. His name refers to all that is true about him, and therefore the totality of his person. Born, not of blood . . . , but of God makes clear that neither physical birth nor ethnic descent nor human effort can make people children of God, but only God's supernatural work (8:41–47; cf. 3:16). This extends the possibility of becoming God's children to Gentiles and not just Jews (11:51–52; cf. 10:16). See also 3:3–8. To all . . . who believed . . . he gave the right indicates that saving faith precedes becoming members of God's family through adoption as his children.

AMR