The differences among those elements are already well answered so I will try to brief you a bit of my researching about Clojure alternatives for people with ASP.NET MVC backgrounds like myself. I suggest you to explore this couple
Caribou
As the own page says:
Caribou is a dynamic web application ecosystem for crafting production ready web inhabitants with minimal effort. Forged in the fire of daily requirements, Caribou is a collection of solutions to problems web developers face every day. The philosophy behind its development is to solve every problem we come across once, in a general way that can be reused over and over. Anything unnecessary or obstructive has been burned away from the wear of constant use.
My resume: a quick environment to model data structures in somehow "object oriented fashion" where you have models and data layer. You would find this more familiar coming from .NET as it provides lot of stuff ready to be used out of the box, even a web interface to play with the models.
Pedestal
Pedestal is a collection of interacting libraries that together create a pathway for developing a specific kind of application. It empowers developers to use Clojure to build internet applications requiring real-time collaboration and targeting multiple platforms.
In short: Pedestal provides a better, cohesive way to build rich client web applications in Clojure.
Clojurists looking for a standard way to build internet applications will love Pedestal. Rather than composing art out of found objects, they will now be able to mold a single, consistent form to match their vision.
My resume: a very functional approach to develop web apps, well designed and powerful but definitely not familiar or similar to ASP.NET, really worth a review
A bit out of topic just to mention Liberator for the sake of completion just in case you fancy to implement REST API's with Clojure.