As Cambridge Dictionary puts it "will" used when referring to something that always or usually happens.
Here is an example: "accidents will happen"
Does it mean that if I use the present simple the meaning will not change, like "accidents happen"?
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That depends on context. If I say, "Accidents will happen", that means that they often happen or generally happen. But if I say, "I will call you after lunch", I mean that I will do this on this one, particular occasion. I might or might not regularly call you after lunch.
Likewise, "Accidents happen" means that they happen regularly. But, "Alice sings today" means that she is singing on this one particular day, not that she necessarily does it regularly.
Really the "one time" is probably the more common use rather than "habitual" for future tense. Present tense ... harder to say. That's often used for "habitual".