As of now, everytime I make a code change, I do a Make, then build (sorry don't have my IDEA IDE handy to get the real names).
But I run the app on tomcat, so the files go to my /output folder during the make/build process. ( i am using maven also).
Is there a single shortcut key that can do both of these? Or do I just need to do a build and it will do both?
i'm newish to IDEA so sorry if I am using the wrong terminology etc.
You can configure this in a "running configuration" (next to the "make" button 
).
I think what you're looking for is an option (checkbox) for "Build on make", which you'll find on the dialog for editing artifacts.
From what the people have mentioned above, most IDE's will come with an option to run your build file and setup multiple configurations, each with different parameters if you would like.
This allows you the option to create a build with/ and without testing.
Unfortunately, I am only familiar with Eclipse IDE, but I cant imagine that IDEA is any different as the posts above have mentioned. I use ANT and Maven and configure both of them to run with tests and without tests to speed up my build process.