The words "I believe X" used to mean "Based on all available evidence I have seen, I'm convinced that X is true". Lately however people have started to use the word to mean any strongly held opinion regardless of any evidence or reason.
To believe something is "to be convinced of the truthfulness of it", to have faith is to have hope in the future based on a belief.
Believe and faith can be misplaced: To be convinced that something is true does not make it true. A conviction which is specific enough maybe testable, a conviction can sometimes be proven or disproven. It is rational to hold convictions which are consistent with available evidence and experiences.
A theology is a (philosophical) theory about gods. A theology may be specific enough to be testable, most however are not. Someone who is convinced that a particular theology is true has a religious conviction or religious believe, which often becomes part of the persons identity or self-identification.
People who share similar theological convictions often join together to form religious groups and religious organizations. One can be convinced either by personally examining the evidence available or by the believing the word of someone who one considers an authority (often as part of the religious organization one is a member of).
The word "god" has also taken on a whole different meaning. The word god used to mean someone with authority and power. For example: In the bible Jezus applies the word "gods" to human judges? By this definition it's obvious that there are gods, many even. [We could then reserve the word "God" (with a capital letter) for the hypothetical entity which has no authority above him. Which leads to the weird conclusion that (this hypothetical) God would be the only true atheist: a-theist, without-god.]
The word "natural" is also confusing. Regardless of what we personally may think: Assume for a moment that the universe was created by someone who was not created. Now we have the situation that the universe is not "natural", but rather "artificial". The only thing natural would be this creator who what no created.
This makes it currently impossible to reason from within science about intelligent design. Intelligent design is not inherently unscientific, but it does challenge some of the most basis assumptions at the basis of modern day science: The unproven (and perhaps unprovable) conviction that Life, the universe and the rest are all purely natural (and not artificial).
The word "supernatural" is also meaningless. Just try to define any observable phenomenon which is neither natural nor artificial? By implicit definition no observable phenomenon could ever be labeled supernatural. Just the fact that we are able to observe it either makes it natural or artificial. Logic leaves no room for anything else.