I noticed that both options are available while running Jboss, and they both recompile the project (I noticed 'make' running with both). I did see this question, the accepted answer made sense, but I wasn't sure what hot-swapping means. What is a possible example of a change which could be registered without needing to restart the server?
Your question needs more details to answer completely, but here are some basic concepts:
Typically, you would hot-swap (eventually manually) .(x)html/.jsp/.jsf/images/.js/.css safely as JBoss doesn't need to process them. Changing code in java classes deployed as .class in a WEB-INF/classes can often be hot-swapped.
Changing code in java files deployed as .jar will almost always need at least redeployment. Some OSGi enabled application server properly configured are more flexible in hot-swapping a complete application (I know Glassfish does but I don't know what specific setting is needed)
Finally, in development, sometimes the multiple redeployments lead to memory leak or unstable application server (often you'll get a OutOfMemory exception in the logs) then you need to cleanup (undeploy, stop, start then deploy)