there are some overlaps but i wouldn't say the political theory is the same even if some of the values may be. they both arrive there for different reasons.

because socalism is generally a precursor to communism and during the cold war, it was the godless communist vs "in god we trust" Christian America. Or at least that is how the narrative goes. and so the religious now tend to see itself as a political force. christianity is a political identity loosely based on being charitable etc but the mixture of politics and religion has created this mutant form of the original Christianity (at least as expressed in the bible).

Though I would hardly say the bible itself is socialist. It is more of a theocratic dictatorship led by an entity named God/Jesus. So in that respect, the bible is not about distributing power equally amongst all, it is subjecting everyone to the one God. Political socialism is the opposite.