Hohomcfo, its very straight forward, though I accept often misunderstood, check out a dictionary.
Deism is the belief in a god who created the world but has since buggered off.
Theism is the belief in a god who is active in the world.
Atheism is the absence of belief in a god.
Religion defines what particular god is believed in and what 'rules' & practices should be adhered to.
Gnosticism is a claim to know something to be true
Agnosticism is the claim to not know if something is true.
So a catholic could be an agnostic theist. i.e. believing but not knowing that the god their religion defines is real. Or they could be a gnostic theist, stating they know 100% that their god exists.
A catholic would also claim to be atheistic about Zeus, i.e. not believing he exists, but likely to go further and say they know he doesn't exist, so to also be gnostic about their disbelief in Zeus.
An atheist, as the 'label' is commonly used, is generally lumped into disbelieving in all gods, from Zeus to Jesus/Jehovah/Yahweh and all in-between. But an atheist is usually not 100% sure about their disbelief in gods and would be an agnostic atheist. Often atheists uncertainty in their disbelief in gods is around the same level as their uncertainty of disbelief in unicorns, faeries, alien abductions, creationism, etc
Some, who knows what percentage, claim to know their is no gods, they would be gnostic atheists, or even anti-theists. There are very few deist religions. But there are religions that aren't theist ie that dont believe in a god. I have even read about some christian religions that dont believe in a god, and I know of a group of practicing catholic priests that dont believe in a god (kept anonymous for obvious reasons).