Facts are made up by humans. If an opinion of mine regarding an empirical argument conforms with the general good of the public I prefer to spend time with, I accept it as a fact. When my opinions contradict with this, I accept that I believe it this way, considering neither options are testable or objectifiable.

I think everyone inhabits a sort of superposition of all possible worlds consistent with their sensory observations. But there are some of those possible worlds with which I identify more strongly—where I feel more myself. So belief is a kind of probability multiplied by self-recognition.

For example: “We believe these truths to be self-evident, that all [people] are created equal”, etc.—it’s not an assertion of objective truth, it’s a declaration of which world we choose to live in.

Belief regards opinions, in which people have a free choice to accept or reject the idea. There is no notion of rightness or wrongness.

Knowledge regards conclusions from a set of axioms, in which people who accept the axioms are honor-bound to accept the conclusions. To reject the conclusion while accepting the axioms would be wrong.

In my life, this governs when I can freely choose and when I am obliged to accept a claim based on whether I’ve accepted previous claims.

That’s a pretty simple distinction, but you’ve asked for us to define abstract concepts without using definitions or abstract concepts. So let’s just say, knowledge is what you know and beliefs are what you believe. A belief implies some level of doubt, while knowledge is just the information you have in your head. There is a lot of overlap. I know that the sun will rise tomorrow, because I understand how the earth rotates and orbits the sun. I believe it will happen because I understand physics and observable phenomena. Put it another way, it is a high-confidence belief based on the knowledge obtained through observation and study. Some beliefs are based on nothing more than hope, and some knowledge is beyond any doubt. I believe the Phillies can win the World Series, but I know our bullpen pitches cantaloupes and our hitters are streaky as shit.

When I challenge my established concepts with new ideas or angles, and realize my previously held truth doesn’t hold up to scrutiny, or is reinforced or expanded upon. For example, “is a hot dog a sandwich?” makes me reconsider how so much depends on context, and how we as humans crave labelling and categorizing to the point of it being detrimental (see biological sex vs gender, Star Trek edit wars, classical music and pornography cataloguing, etc)

Knowledge is what happens when you’ve evaluated enough evidence to reject the null hypothesis that something is false. If you haven’t seen the evidence, but still think it’s true or false (you don’t lack belief), then you have a belief about it. As such, knowledge is a type of belief with extra justification.

If I’ve reviewed enough evidence I’m comfortable saying I can reject the null hypothesis, that is I have a belief that it’s knowledge, I’ll call it as such. If I haven’t, I’ll couch my confidence in my belief accordingly.

I want to know how it works in real life for you.

What works for me in real life is know as little as possible, view all beliefs as clouds moving across the sky

I know I exist. Everything else is varying levels of belief.

I’m a Marxist-Leninist, so the dialectical theory of knowledge. What starts as ideas are tested and confirmed or denied in reality, which then sharpens ideas to be retested and confirmed or denied in reality. Ideas come from real, material conditions, and it is through this cycle that theory meets practice, sharpening each more effectively.

Knowledge can be externally verified by an independent party.

Belief can be corroborated but not verified.

For me it’s the difference between a preponderance of evidence suggesting such, and something being applied and proven until any doubt is removed.

For example, I was trying to find studs in drywall recently (last house was plaster and lathe), and looking at things Socratically, I could use a stud finder but I might be drilling into conduit or a pipe. So I was like “I can use magnets to hit drywall screws to try to confirm the presence of a stud”, and it seems reasonable, but I’ve never attempted it in practice, and there could be all sorts of things a magnet could hit, since I’ve no experience with drywall, how close a steel pipe could be, any of that. So it’s a belief. It’d be rather arrogant of me to accept this as a reliable method without testing this method, drill through a pipe and wind up with egg on my face.

So, I tested this by getting two magnets to stick vertically, then measured 16" out, got 2 more magnets to stick vertically, kept doing that until I hit half a dozen spots, all 16" apart. Drilled a pilot hole, felt resistance and the smell of wood, drilled a couple more.

I think somewhere between mounting a flat screen to fixing 3 closet shelves it became knowledge, not sure exactly when, but all the doubts were removed and it never blew up in my face. I can just waltz in a room and sink a bunch of holes in the right spot now without being skeptical of some electronic stud finder.

I guess what I mean to say is that testing something and having it consistently work and be reproducible is what leads to knowledge imo

I think this is a really interesting question. To me, if I hear a claim, I might say I accept it as knowledge or believe it as a worldview.

For example, I get irked by people asking if I “believe” in climate change. To me, it’s not a matter of belief: there is a body of knowledge being scrutinised by extraordinarily smart and talented people. I accept the existence of and need to mitigate climate change.

On the other hand, do I believe we’re not alone in the universe? I can’t rely on knowledge, it’s a lot of intuition.

I define it by whether something is independently verifiable.

I am told that there are 8* planets in our solar system, and where they are located. If I wanted to, I could buy a big telescope, point it at the sky and find all 8.

I am told that it is possible to boil water through nuclear fission. If I had the means, I could take a number of resources, spend decades researching nuclear physics, build my own test reactor, and verify that this is possible.

I am told that the earth is flat. I could get a pilots license, buy a plane, and fly to Antarctica to see the ice wall. I would find that there is no ice wall, just a number of scientists who are very passionate about ice samples. Therefore, it is not independently verifyable.

I don’t have the money to verify all of these claims, but they are all claims that have been verified by hundreds, if not thousands of independent people and organizations throughout history.

Probably doesn’t answer your question completely, but I’m a big fan of the phrase "my understanding is . . . " In other words, this is what I “know” as fact, but I’m aware that my knowledge could be wrong or insufficient and I’m willing to be corrected or updated. I use this phrase almost any time I’m asserting something as fact, as a kind of cya.

Belief is when a claim comes from a source I trust. In some cases, it’s a source I’m choosing to trust.

Like, my nephew is staying with me. He’s had meth issues in the past. His alternative is a shelter. He claims that he has a seizure disorder, and that puts me in a difficult spot because he says it gets worse on the street and also in shelters.

That’s pretty believable, but there’s a part of me that’s aware it could be a manipulation, this whole claim. I haven’t asked for evidence, despite the feeling of doubt.

This is a belief of mine. I am choosing to believe his claim.

If he were to show me authenticatable hospital paperwork documenting the seizure disorder, then it would be knowledge. Then I would know.

This is an example of the difference between the two in my own life right now. It’s a belief because to a certain degree I’m taking his word for it.

Incidentally this is the same way I think the word works in religion. People believe in God because they choose to. I feel like I know God exists, because I’ve encountered it during mushroom trips. But others, who haven’t had those direct contact experiences, believe.