Deism is theism; if you believe that any kind of deity exists, you're a theist. The distinction is that deists are generally not religious. I don't even know how a deist COULD BE religious...
There are all kinds of definitions of atheism, but I've settled on the one which appeals to Greek etymology. Theism is about belief, and gnosticism is about knowledge. It's possible for someone to believe a god exists without knowing it for a fact, so that person would be an agnostic theist; someone who doesn't believe in gods because he claims to know that no gods exist would be a gnostic atheist.
In practice, most atheists are agnostic atheists. Most of us don't believe gods exist, but we're not 100% certain of this. This is the category I fall into, and by my last count, it's the category most of us here fall into as well.
Sometimes, like in discussions of 18th & 19th-century philosophy, historians define "theism"
not as the belief in God, period, but as the belief in an active, purposeful, interventional god (as opposed to the god of deism, which is none of those things). That would mean that both theism and deism are sub-sets of "belief in a god of any kind," and then we would want to supply some handy name for that, since 'theism' was taken ('Goddism'?), but I don't know if anybody ever did supply one. Look at it this way, we have three sets:
A) All those who believe in god
B) All those, within A, who believe that God is purposeful and intervenes in the universe
C) All those, within A, who do not believe that God is purposeful and intervenes in the universe.
Everybody calls C "deism." But if "theism" is the word for A, what's the word for B? And if theism is the word for B, what's the word for A?
It's all semantics, obviously. The historians use the terms which are more convenient for them, and we use those which are more convenient for us, and as long as we make clear how we're using them, it's all good.