Difference between make and build in Android Studio

The difference is that Rebuild executes gradle's clean task first. If you look in the Gradle Console 'Rebuild Project' will say something like

Executing tasks: [clean, :app:compileDebugSources, :app:compileDebugAndroidTestSources]

While 'Make Project' won't have clean

Executing tasks: [:app:compileDebugSources, :app:compileDebugAndroidTestSources]

Most of the time you should use Make Project. Sometimes, after adding libraries and making big changes to the project you should use Rebuild Project.

If you look at the menu, you'll see that Make Project and Compile have keyboard shortcuts, that suggests that they are often used. Others are seldom used.

It is the same as IntelliJ Idea.

Compile All the source files in the specified scope are compiled. The scope in this case may be a file, a package, etc.

Make Project All the source files in the entire project that have been modified since the last compilation are compiled. Dependent source files, if appropriate, are also compiled. Additionally, the tasks tied to the compilation or make process on modified sources are performed. For example, EJB validation is performed if the corresponding option is enabled on the Validation page.

Make Module Compiled are all the source files that have been modified since the last compilation in the selected module as well as in all the modules it depends on recursively.

Rebuild Project All the source files in the project are recompiled. This may be necessary when the classpath entries have changed, for example, SDKs or libraries being used added, removed or altered

Copied from IntelliJ Idea 13 help.

Difference between make and rebuild is "clean" task.

When you do rebuild project it performs clean too.