I know that an application is a program that you interact with on the desktop, but what exactly are processes and services? Are services classified as processes or is it the other way round?
Application: Application software, also known as an application or an app, is computer software designed to help the user to perform specific tasks. So, you are right. An application is something that the user interacts with.
Process: A computer program is a passive collection of instructions; a process is the actual execution of those instructions. Several processes may be associated with the same program; for example, opening up several instances of the same program often means more than one process is being executed.
Processes then, is what is actually making the application do something.
Service: Local implementations in software. Basically, a service is something that is usually built into the OS itself, and is designed to not have any user interaction.
Examples This is really how it works. You have an Application. You launch the application, the app is programmed to do things. How the app accomplishes that is by using processes. An app could use more if it wants to perform larger tasks. Meanwhile, say Windows or Mac has services running. These are things that other apps or only built in apps can handle. It is usually required to keep something running, but is not available without it.
Keep in mind, a lot of people (Including Developers), will refer to their apps that run in the background as services. They are not. Only the OS itself can create services... Actually, services can be created, but they are usually meant to be used for many different kinds of apps.
Hope that clears that up a little bit. If anyone has a correction let me know.
This web page gives a detailed comparison of a service Vs an application in Windows from Windows Vista and above: http://securityinternals.blogspot.ae/2014/01/difference-between-windows-service-and.html