What is the ruling on one who differentiates between an atheist and a polytheist, while believing in the disbelief of both, and what is the ruling on one who hates children?

The distinction between an atheist and a polytheist is correct; both are disbelievers. An atheist is broader in meaning than a polytheist. A polytheist might believe in God but associate others with Him, and this could be considered a form of atheism. However, an atheist, in the broader sense, is one who denies the existence of Allah the Almighty, views the universe as having no Creator, and denies the afterlife. Procreation is one of the greatest objectives of marriage, and the Prophet, peace and blessings be upon him, commanded choosing a loving and fertile wife. Disliking the procreation of children due to fear of sustenance indicates a weakness in faith regarding Allah's provision.