Research and understanding of the various Loyalist groups in Northern Ireland is limited. I am ashamed to admit that I've only recently begun to delve into this fascinating and shadowy history. The UVF formed in 1966 as a spiritual successor to the original UVF that fought Home Rule in the early decades of the twentieth century. The new-UVF sought to stand as a deterrent to the growing Nationalist sentiment (bolstered by the 50-year anniversary of the Easter Rising) and Civil Rights movement in the North. They utilized violence toward these means. The UDA was a reactionary group formed to fight the Provisional IRA. They originally sought complete independence for Northern Ireland which was counter to the goal of British unity that the UVF fought for. Structure of the two groups were quite different: UVF was similar to the PIRA in that there was a central leadership that all brigades reported to, while the UDA was devolved with six separate brigades that worked together.

To me, Carolyn Gallaher described these two groups best:

To most observers, political Loyalism is associated with the UVF, whereas revanchism is connected to the UDA.

My knowledge is limited on this subject but hopefully this gives a brief answer. Gallaher's After the Peace is a great place to start (it's what I am finishing at the moment).