I think they are two different things, yet similar in many circumstances.
CD tends to look at the natural aspect of religion and the world around us. It is focused more on human reason and understanding in order to see God's miracles in creation. CD tend to be skeptical of "revealed" religions where a lone prophet claims to speak the word of God (or gods). CD is classified as a natural religion.
CH is more about serving and helping humanity. Humans are good, deserve life and all have basic needs that need to be met. It is more of a philosophy (like Buddhism), not a religion.
Both use Jesus as a mentor and strive to follow His teachings. Both have no problem with science explaining things. Both tend to disregard the supernatural.
It is possible to be a Christian Deist Humanist...if you are big on labels.
Thank you for your perspectives.
My response here is more about the topic in general as well as thoughts skimming the surface of my sleepy brain in regards to the thread..... Sorry in advance if it's not that organized or clear. It's late and I ramble when I'm tired.
Fundamentalists who want to promote a revisionary version of history perpetually claim the Founding Fathers of the United States who were Deists were actually Christians and insist the two are synonymous because it suits their agenda for them to be. One of my first experiences on this site was on a thread where this man passionately insisted Thomas Jefferson was a Christian Deist (which to him was on par with his own conservative Baptist beliefs) and engaged in a lengthy lock of horns with another poster over it. Some people put much more effort into winning a point than acquiring facts, knowledge, and understanding. I think Deism as it was followed by those leaders at that time was not Christianity because it denied the basic tenets of the Christian faith, which is that Jesus Christ was not merely a mortal man who had enlightened philosophies about ethics, but a divine deity, the son of God who was sent here to be our Savior. Until your OP I was under the impression that Christian Deism still disbelieved the divinity of Christ but revered his teachings and strived to emulate them, and believed on faith in God as the creator. The foundational qualification of a Christian religion is the acceptance of the divinity of Christ. Belief in God without belief in the deity of Christ is still religious in nature, but not Christianity. Conversely, to me, if a humanist accepts the divinity of Christ she's still on a branch of Christian faith even if more of the focus is on humanist principles. I went to an Ethical Culture (humanist) school when we lived in NYC, primarily because there was a lack of academically strong Christian schools there, and it appealed to my family that ECFS focuses on ethics that were parallel to Christ's teachings about how to treat others with kindness, compassion, dignity and respect. So, I've kinda grown up in my own unlabeled brew of Protestant Christianity and humanism. I'm a member of a liberal-leaning Presbyterian church, so I simply picked that label since I had to pick one here.
Anyhoo. Personally, I'm not keen on labels. All denominations and philosophies have essentially been an amalgam of beliefs, many of which had previously been disparate and seemingly paradoxical but are made cohesive, congruent. I've been on a Kierkegaard kick lately, so what comes to mind is a quote about how once you label someone you negate them. I think it's true. Labels have clear definitions that form boundaries, and when they are affixed to people, it creates an expectation that the person's beliefs and characteristics will fit within the parameters of that label. It neutralizes the individuality of a person. Confusions and disagreements then sprout up when the identifying labels are the same on the front but have different lists of ingredients when examined. I do understand why they can be helpful at identifying matters and understanding them, but I think care has to be used when applying and when reading them on people and forming presumptions about them. That's especially true when it comes to labels relating to religion, I think. There's a myriad of interpretations of the Bible that lead to divergent meanings of it, so the understanding we're accustomed to or associate with a label might vary considerably. Mainly, I think we should focus more on what people do than what they say they are or what we think they are based on their labels. We have to explore, examine and contemplate beliefs and run them through the filters of our brains and our hearts to see if they make it into becoming who we are. We need to believe what we believe and reject what we don't and not make it any more or less complicated than that. I don't think we're meant to just believe what our parents believe or what the labels say to believe or what a political leader or writer or philosopher believed or how someone else believes religious doctrine should be believed. Besides, the ones who really challenge society and push forward progress are the ones who don't stay within the boxes of what they've been labeled. Jesus didn't wear the Christian label because it didn't exist then. He was Jewish, but of course today a Jewish Christian would be another disputed paradox. He just lived out his purpose.
Like I said, I babble like crazy when I'm tired..... Hope this makes some sort of sense.