The relationship between the two rivals has ebbed and flowed throughout the years. They first worked together in their early years where a professional relationship had been established. When Microsoft and Apple worked together, they shared information freely and appeared to have a good working relationship. It was not until Gates introduced the first version of Windows, which borrowed heavily from the interfacing graphic technology developed with Jobs.
At this point, Jobs and Gates’s relationship was damaged because Jobs felt as though a lot of the technology that went into developing Windows was borrowed (he felt stolen) from Apple. Jobs was angry, but Gates did not care because he felt the idea was big enough that Jobs did not have exclusive rights to the idea. This was probably the disagreement that put a permanent wedge between the two.
However, this was just the spark that created the rift as over the years. At some point, though, the rift subsided with Jobs getting funding from Microsoft to keep the company afloat. The relationship is a mix of mutual respect but allows for each to disagree with each other. The two often criticized their approaches to technologies, but at some point they buried the hatchet—not quite rekindling their friendship but not being enemies either. Toward the end, it was probably a relationship of mutual respect.