Your pairing is not helpful for understanding.
Someone will clean the windows over the weekend
does not mean that someone other than the speaker will clean the windows. It is merely a prediction that the speaker, the speaker and one or more others, one person other than the speaker, or several people not including the speaker will clean the windows. Who will clean the windows is simply not specified. It is a vague sentence.
I will have someone clean the windows over the weekend
announces the determination of the speaker to arrange for some unspecified person or persons to clean the windows. It implies that the speaker will not personally do it, but it does not absolutely preclude the speaker from doing it. Who will clean the windows is again not specified. It is not vague, however, about who will take sufficient action to make sure that someone cleans the windows. It is still a rather vague sentence, but less vague than the first.
Basically, the future says that some task will be done; the causative says that arrangements will be made so that some task will be done. Both can be used in a way that leaves unspecified who will actually do the task, but usually the implication of the causative is that the subject of the verb will only arrange for performance of the task by someone else.
All this vagueness is not necessary.
John will clean the windows
and
I will have John clean the windows
are not vague as to who will do the task. In both cases, the prediction is that John will, The causative implies something more, namely that I will do the task of arranging for John to clean the windows.
Thus, there usually is a difference between the future and the causative but you said
Someone will clean the windows for us
That sentence is merely a prediction that the windows will be cleaned, but the "for us" implies that whoever will do it is not among us. Moreover, it does not even explicitly commit "us" to arranging that it will be done. That sentence is vagueness piled on vagueness.
By the way, the American idiom is "over the weekend" or "on the weekend" or even "during the weekend" rather than "at the weekend."
EDIT In response to the OP's comment
I'm going to have John clean the windows
may mean
I have already decided that John will clean the windows
or
I will arrange for John to clean the windows
The causative
I will have John clean the windows
means, for a careful speaker, that I have not yet asked, ordered, or otherwise arranged for John to clean the windows but have already decided that John will do so. Otherwise, what would be said by a careful speaker is something like
I have [ordered/asked/scheduled] John to clean the windows.
Now it is clear that my actions were in the past even though John's part is in the future. We would not use a past causative with a future event.
Part of the problem with this whole discussion is that although the English tense system is capable of great subtlety of meaning, we usually do not rely solely on that system to convey those subtleties. It is too easy for the speaker to misspeak or the listener to mishear. The sentences that you are working with seem to place the entire meaning on tense.