I'm guessing that the descriptions you have seen are from fields that work very differently from math and cs, including AI.
In the social sciences and most of the physical sciences, an hypothesis is a statement that might be true or false. It is stated in a certain way for technical reasons, but it is normally stated at the beginning of a study before there is any evidence whether the hypothesis is true or false. Depending on the field, some methodology is used to gather evidence about whether the hypothesis is true (accept) or false (reject).
The reason for proceeding this way is that the gathering of evidence, say with experiments or questionnaires, is an expensive and time consuming endeavor that is actually guided by the statement of the hypothesis. For example, if the research is guided by questionnaires to people, you don't ask the people a lot of random questions and try then to figure out what it means. You ask them questions related to the hypothesis so that certain answers (determined in advance) support the hypothesis and the opposite answers work to refute it.
But math and much of cs works differently. We have an idea for a theorem, or a way to improve garbage collection (GC) in a programming language. We work to prove that theorem or build a program to test out the idea. If we prove the theorem we have the basis for a (part of a) paper. In the GC case, we run the program to see if it is an improvement over other known approaches or not. This gives the basis of a paper, perhaps.
But, we don't usually call the (possible) theorem or the idea for GC the hypothesis, though in some sense it is. But in both math and CS you often just try something to see how it works out. Note that the trying out is actually the gathering of information and it may come before the "hypothesis" (theorem or gc idea) is ever stated. The time scale is often reversed.
Another way to say it is that we often start with an informal idea (rather than a formal statement), work on the idea and if we learn something, only then make a formal statement. The social and other similar sciences normally don't work that way, or at least don't present their work as if they did.
In fact, though, a social scientist will him/herself need to have that bright idea first about what might be worth studying, just as a mathematician does. But they will still state a formal hypothesis to guide their actual experimentation.
I'm guessing that you are puzzled by this since the formal hypothesis idea seems a bit foreign to what you see in papers. You are likely to see first the "idea" that drove the research, then the proof of concept experiment (a program, perhaps), and finally the conclusions. Not hypothesis is stated, and it isn't expected, though it could be formulated that way. But since the work was done before the hypothesis was formulated, there is no real notion of accepting or rejecting something stated in advance.
The difference is actually driven by the different kinds of evidence required in order to find truth that advances a particular field.
