It seems all four of these branches of design relate to each other at one point or another, and one can easily be confused for another by novices or outsiders looking in. Job postings online frequently interchange the terms for job openings, yet explain similar descriptions of job duties.
In reality, there's no difference between jobs with those different titles (except that "web designer" is limited to projects on, well, the web).
In theory, the terms refer to different aspects of the design discipline. Following are three different explanations I've read:
Jesse James Garret draws a line between interaction design and interface design as the degree to which the design has been implemented. Interaction design deals with the structure of the site, while interface design deals with the skeleton (creating concrete representations of the structure created by interaction design). Garrett has a famous diagram that shows how some of the roles are related.
There is the philosophical notion and then there is how the roles differ in the job market.
Web Design concerns the look in feel of the website as far as Marketing and Branding and browser standards.
Interaction Design concerns the user behaviors and actions during a user flow of an interface (ie: How the widget works, how it slides up or overlays, drops down, and very specific tasks that lead to user objectives and needs).
User Experience Design concerns the overall discipline of studying users and how they use interfaces and even tangible products, but with an emphasis on user research and user centric design in contrast to just Marketing Design. A UX designer will drive the project from Research, Information Architecture, Interaction Design, Visual Design, and Testing, giving broad direction to the team.
User Interface Design concerns with the visual design of specific widgets icons buttons, creating style guides, and pixel perfect designs with a more user centric view than just general web design. It's also not just limited to the web. UI design is more on going as many widgets and add-ons are constantly created on many tech sites.