Aren’t regeneration and
conversion the same thing?

No, they are not. Confusing these two very different things has led to many heresies. Regeneration is God’s supernatural, omnipotent, instantaneous, creative work to give a rebel sinner a new nature that loves Him and wants to serve Him. Conversion is the lifelong educational process of a one of these regenerate persons coming to know God and the truth of the gospel for his comfort and knowledge and for how he should live in the world to please God.

For a short study of regeneration and conversion … https://letgodbetrue.com/sermons/index/year-2017/regeneration-conversion/.
For a comparison of regeneration and conversion … https://letgodbetrue.com/sermons/index/year-2006/regeneration-conversion-compared/.
For the full truth about being born again … https://letgodbetrue.com/sermons/index/year-2002/born-again-truth/.