What do "Installed", "Running", and "All" apps mean in Android Settings? I have an Android device running on Android 4.4.4. In the Settings, I have no idea what "Installed", "Running", and "All" apps are.

What do those mean?
The menu in Settings › Apps usually has multiple tabs (or items in a drop-down), signifying a (sub) group of the apps available on your device:


Installed: user-installed apps. Most of them are those you installed yourself, but some might be "vendor-provided" apps that got installed on initialization (first use or after a factory-reset). These are the apps you also can uninstall.
All: All apps, whether pre-installed or user-installed. This is the only group where (pre-installed) system apps are shown as well; these you normally cannot uninstall, but only disable (and sometimes not even that).
Running: These are the apps currently running – either because you started them explicitly, or because they got started by some intent (in most cases, this is BOOT_COMPLETED, i.e. apps starting automatically after boot – but it also could be something else they're reacting on, such as network state changed, or some other app calling them as it often is the case with Maps)
Disabled: On some devices, you might see this as explicit section listing the (system) apps you've disabled. On other devices, this section might be missing; disabled apps then carry the string "disabled" next to their names in the "All" section.