Mend, repair, patch, rebuild are comparable when they mean to put into good or fitting order something that is injured, damaged, or defective.
Mend basically implies a freeing from faults or defects, but in its most common use it specifically suggests a process of making whole or sound something that has been broken, torn, or injured (as by wear or use). In such use the term is especially applicable when the task calls for no extraordinary skill or unusual equipment; thus, one mends a dress by sewing up tears, darning holes, or reinforcing worn spots. Often, and especially in extended use, mend stresses the resulting putting in order without much regard to the nature of the means of its attainment.
Repair is often interchangeable with mend in the sense of to make whole or sound, but typically it implies greater or more professional skill by the performer and usually correspondingly greater complexity both in the task involved and in the equipment used; thus, an old-time cobbler mended shoes so that they were good for further use but a modern specialist may repair them so well that his work cannot be detected; a boy may know how to repair a car but be unable to do so for lack of essential tools.
In extended use, too, repair may be quite like mend, but often it more specifically implies a making good or making up for something.
Patch basically implies a mending by covering, filling in, or reinforcing such a defect as a hole, rent, or weak spot, typically with the same or a similar material.
Sometimes, often with up , it implies careless, hurried, clumsy, or temporary mending and in much of its extended use this is the aspect stressed. Sometimes, often with together , patch implies a making from bits and pieces or odds and ends.
Rebuild, which normally means to build again something which has been razed or ruined, is often preferred in industry and business to repair because it implies a thoroughgoing repairing with addition of new parts when necessary that makes a thing like new.