This question is an important one because it directly impacts whether or not we even understand what unity is. I'm convinced that a better understanding of unity within the body will lead to an increase in actual unity of the body.
What is uniformity? Uniformity is the demand that everyone in a group thinks and acts the same way. It allows for little to no variation. A good example of this is the military. Everyone is basically expected to think and act the same. If any variation exists, it is both small and inconsequential.
Is uniformity the same as unity? In a word - NO.
What then is unity? I suppose we could come up with a number of definitions. Here's mine: unity is a togetherness of mind and spirit that looks to the good of the group without demanding sameness within the group. Any group of any kind can have unity. The church is only one of many. However, since the church is led by the Holy Spirit, it should be easier for the church to have unity than any other sort of group. How sad it is, then, that the church struggles so much to be united.
One thing that leads to this struggle for unity is the faulty expectation of uniformity. When we look in the bible, we don't ever read demands for uniformity. For example, only a relatively small number of core doctrines must be believed in order for a person to be part of the church. As for what we might refer to as secondary doctrines, there's no demand for uniformity. We appear to have some measure of freedom in what we believe about these. We are never told that unity can or should be sacrificed over non-salvation issue doctrines.
Another issue is worship style. Related to this is music. Frankly, these don't really matter when the church gathers. As far as I'm concerned, just do whatever is edifying in the Lord. Just don't let preferences get in the way of unity.
As the body of Christ, if we are truly looking out for the good of others then we will be united. I might hold many differences in doctrine and/or practice with a brother, but if I am striving to edify him in Christ, then those differences won't really matter. However, if I demand that we believe and act exactly the same way, it will actually drive a wedge between us.
Striving for uniformity leads to division.
Striving for unity leads, not surprisingly, to unity.
In the end we see that unity and uniformity are actually closer to being opposite than the same. Because of this, let's jettison any expectations of uniformity within the family of Christ. Instead, let's live united despite our differences.