UX design process usually follows the prototype in an informal or formal usability testing process. This process happens before and even after launching of the website. This UX design helps to rectify some complexities in some kind of websites like multiple user, merger or acquisition and all.
UI design process most likely to interface human and designs. Which concentrate mainly on the front-end development, like tasks, workflows, more obviously simplifies whatever appears complex. As a result, it plays a role of bridge to connect programming and designing.
As the web design working on creative concepts, interactivity, color theory. The web designers work is not less than a graphic designer, and most probably, the knowledge of HTML and Javascript coding is additional. While coming under responsive web design this is the additional web development and entirely different range in designing version. The name itself delivers the meaning for this process, that is it auto-simplifies the layout designs according to smartphone, computer or tablet screens, like 4 column layout of 1292 pixels into 2 column layout of 1025 pixels. In other words, this responsive designing is called as context-aware.
Thus these three are the main branches of web design family tree, all these three plays a remarkable work on its own for the best experience of the user.