It is often assumed that Civil War soldiers wore a strict uniform, in that all the members of a regiment wore similar coats, breeches, hats and so on, as was typical of later armies. In actual fact, the evidence for this is limited at best. Although there are some well known mass issues of uniform clothing, for example that to the Oxford Army in 1643, it appears that many units never received a uniform as such, although in some cases they may have been given captured civilian or military clothing items. Even when a unit had an existing uniform, there is evidence that new issues of clothing could be of different colour to that received before.
Even if we assume that a unit had a uniform, this still leads to two further questions. Firstly, how uniform was it? More modern contracts were normally to a single supplier, and often produced in a single factory. Supplies to make the items were ordered in a similar fashion, and it is possible to see from this that, for example, thousands of almost identical coats could easily be supplied.
During the Civil War, however, a contractor faced with such an order would have sub-contracted with a number of suppliers, who would have in turn sub-contracted part of the work. With probably hundreds of individual makers working on the contract there is liable to have been considerable variations in the details of the coats produced, as each carried out the work in their own way, and sought individual shortcuts to boost profits. When you add the fact that there would have been variation in the cloth used, the dye batches, and such details as buttons, etc even a "uniform" item could end up significantly different from the one next to it. In the case of the Oxford Army issue the soldiers seem to have been issued with coats and breeches of the same colour (although it is unlikely that they were actually from the same bolt of cloth, so may be significantly different in colour and texture), but in general this seems to be rare. There seems to be no evidence for soldiers being issued with uniform coloured breeches in a different colour to the coat, and indeed some contracts specifically accept variation in breeches colour, so it seems that uniform breeches were rarer than uniform coats. Other items such as hats (unless provided with a suit, as in the Oxford Army Issue) and stockings are even less likely to be uniform.