conviction, working hypothesis, received wisdom... Yes, each of those words have different, significant, meanings and using them indiscriminately or inattentively tends to lead to misunderstanding.
We need trust - both to trust [select] other people and to earn the trust of others.
We need to believe - at least conditionally - experts, elders and instructors who have information we lack. We can't each research every area of knowledge and learn every skill required to get through life in a technologically complex society.
We need to obey - whether we believe in all of them or not - a set of external rules, such as traffic signage and city bylaws, that we can rely on other people to obey as well, to prevent chaos. We also need some conventions, like "please and thank you", stopping for pedestrians, not spitting on the floor, that most of us believe in strongly enough to make human community bearable.
We need a coherent set of internal rules to steer the moral course of our interaction with other people and the world. These are our convictions. Whether founded on the moral teaching of the OT or folk wisdom or 20th century political philosophy, this set of rules is compiled by each thinking person, after reflection and in the light of learning and experience, as interpreted through feelings. It's a complex structure - for some, a fragile one. Build it well, keep it in good repair, and it can withstand doubt, disillusionment, derision and even the victory of right-wing parties in federal elections.