difference between “find ” and “fibd out”

I think of the difference as: "Find" is for literally finding, as in locating, an object. "Find out" is more like discovering, realizing, or learning information. "I found my lunch wasn't in the fridge" = "I looked in the fridge and my lunch wasn't there." The meaning of "found" is very specific. "I found out my lunch wasn't in the fridge" = "I expected to find my lunch in the fridge, but it wasn't there" or "Someone told me that my lunch wasn't in the fridge." The meaning of "found out" is not as specific and context matters more, but it has more to do with information ("my lunch wasn't there") than the real thing ("my lunch").

Find means you located or retrieved something that you might have been looking for. Find out means discover or realize.

I'd use the first when I just open the fridge and look and nothing is there. The second could theoretically work if you're out of the house or if you think there might be food but then discover that, in fact, there is no food. Find is better when something is lost and then located--> found. Find out is better when you learn or discover something new.

If someone told me they found nothing in their fridge, I would assume they looked in their fridge and they did not see anything.  If someone told me they found out that there's nothing in their fridge, I'd assume someone told them or they became aware secondhand.