According to Webster's New World Dictionary, to think is to hold or have in the mind, conceive; to hold in one's opinion, judge, consider. To believe is to take as real, true, etc,; to have confidence in a statement. Belief implies mental acceptance of something as true, even though absolute certainty may be absent. To know is to have a clear perception or understanding of; be sure or well informed about. Faith implies complete, unquestioning acceptance of something, even in the absence of proof and especially of something not supported by reason. Statements that are true or false by virtue only of the meanings of their constituent terms are called analytic truths or falsehoods. Unless stated otherwise, the term truth claim in this essay will refer to non-analytic (synthetic) truth claims.
Thinking is the broadest category encompassing belief, knowing, and faith (plus other types of thoughts such as desire etc.). Belief is the next broadest category encompassing faith, opinions, views, convictions, persuasions, sentiments etc. The term know is preferred over belief when referencing facts. So a diagram of the relationships would consist of a large circle for thinking with two medium size circles inside thinking, one for believing and one for knowing and a smaller circle inside believing for faith. Some truth claims are contigent facts, facts because the evidence is plentiful and consistent in support of the truth claim but contigent because the evidence is incomplete, and this can be incorporated into the diagram by overlapping the believing and knowing circles. Rationalists and skeptics will keep the knowing and faith circles separate. This is not meant to be all inclusive. Omitted for simplicity are numerous related concepts like trust, confidence, credence, etc.
The knowing circle contains fact claims, including analytic truth claims, all of which are either true or false. All other truth claims are beliefs. No matter how rational, reasonable, sensible, and logical a truth claim may be, if it is not proven (and not an analytic truth or falsehood) then it is a belief. Beliefs can be absurd or reasonable. All beliefs are not equal.
We can adopt a belief or not, we have no obligation to hold particular beliefs. However, if we want our decision making to be deliberate and informed despite incomplete factual information then we must adopt relevant beliefs. False beliefs can sometimes be productive and true beliefs can sometimes lead us astray. Yet true beliefs are ultimately more effective guides than false beliefs.
For every true belief there are many competing false beliefs. So we have an obligation to make sure our beliefs are justified by, and well rooted in, good evidence. We also have an ethical responsibility to avoid mistaking our unproven beliefs for proven facts or "Truth", to take personal ownership/responsibility for our beliefs and their consequences, to recognize the provisionality and element of uncertainty inherent in belief, to consider alternative explanations and explore the full range of evidence that relate to our beliefs and to employ valid logic in constructing our beliefs.
That which is real or true can be unpleasant. It is true that we all die, usually within about 100 years of being born. So seeking happiness can be at cross purposes with belief's purpose of identifying what is true or real. Accordingly, we need to resist the temptation of wishful thinking when adopting our beliefs.
Our desire to explain what we don't know is strong. This desire can motivate people to adopt as their belief a declaration that superficially provides the appearance of explanation even when it lacks the substance of explanation. Our knowledge about the world is limited. We do not have explanations for many phenomena including the big question of existence. Accordingly, we need to resist the temptation of promiscuously adopting beliefs to disguise our ignorance.
Belief is a label and like all labels we can use it correctly, incorrectly, or not use it at all. We have a belief every time we mentally accept an unproven truth claim as true (or false) independently of whether or not we acknowledge the belief as such. In an unusually intelligent but fatally flawed essay that argues that beliefs are bad and unnecessary, a fellow atheist Mr. Jim Walker incorrectly claims, among other things, that if we deny we have beliefs then ipso facto we don't have beliefs. Arguing that the claims that have a so-called "no belief" status are somehow the better claims, as Mr. Walker and others do, when taken to its logical conclusion is equivalent to arguing that the best claims are those that are the most naive, ignorant, and empty like those of a newborn baby's. By the mere act of accepting or rejecting an unproven truth claim we adopt a belief. Every adult should have many thousands of beliefs and no adult could function competently otherwise.
If you have read Jim Walker's article then you may be asking: What about opinions, views, convictions, persuasions, and sentiments? Do we need these at all? The article Problems with opinions, views, convictions, persuasions, and sentiments suggests that one need not own any opinions, views, convictions, persuasions, or sentiments to establish scientific facts, or to live a fulfilling moral life. Living without beliefs by itself is insufficient to eliminate intransigence, prejudice and dangerous superstitious thought. Take non-ownership of beliefs to the next level and deny ownership responsibility for all judgments one holds as true!