Essentially, concepts are different from words. Words are symbolism that we use to hint at concepts. In using words, we play a game of charades from which the other person tries to guess what concept is being presented. In this use of words the words are disposable tools who's value is only in hinting at concepts.
People's use of words in each discussion, generally imply what meanings they are suggesting by their use of words. In effect, they are saying "I am going to use this word to mean this and this words to mean this".
Since discussions are in the context of other discussions, the word meanings that were suggested come to be referenced, which makes the temporarily chosen word meanings significant.
There is significance to various uses of the word belief.
When I hear people using the word faith it usually implies an intention to think something is true. In that case it is used from the perspective of someone who is concerned about potentially not believing something. It is like "hope" but without the implied possibility that hopes might be dashed. It is a an intentional belief that one hopes to have.
In talking about recovery and mental health, a common topic is things that people think (or accept) without necessarily knowing that they think it. A useful term for that is belief. Because, people say "we came to believe that a power greather than ourselves....". Or, people refer to their irrational beliefs and overcoming them.
It implies that there is work beyond reasoning about a concept, to deal with the belief.
Often, belief in this sense is refered to without it being acknowledged that we can believe things without noticing it. Belief then can be confused with reasoning and people think that they just need to understand some concept and then they will achieve the belief. Or they think they just need to hope themselves into the belief by repeating a phrase over and over and they will achieve the belief. Or, they are frustrated that someone else has a belief when they have offered them the reasoned argument that challenges the concept that they think is the other person's belief
The belief I'm referring to is unintentional and so one trains themselves to acquire or overcome the belief. It is not accessible by reason.
A part of our mentality that is greater than our chattering/reasoning self forms our beliefs. Some sanity is achieved through instances in which we admit that our reasoning self is powerless over that greater part of our mentality. This is the approach of REBT, though it is not usually described that way. It is also the approach of AA in some senses when one admits they are powerless.
REBT describes our behaviors as something that we regulate through training ourselves, rather than simply talking about some concept. Our behaviors are based on our beliefs which are unintentional.