The file manager only shows "public" files in the internal storage. It doesn't show apps, doesn't show app's "private" data (most of the data apps store), doesn't show any of the system partitions (where the operating system, radio firmware, bootloader and all of the stuff that makes the phone actually work live). Basically if you want to undertand what is using space, a file manager is of very little use.
So start from the system storage settings. They can be misleading and unhelpful in some ways (and exactly which ways can differ between phones), but they'll give you some idea. A 16GB Samsung immediately after a factory reset probably has about 10GB available: the rest is taken by the system (this is true for all computing devices: they quote the total storage, not what's available to the user after you take out the bit needed by the system). You are "guessing" that 2-3 GB is taken by apps: if you are right that means you don't have or use many web browsers, social media apps, etc. What does the storage menu tell you? Go into Settings > Apps and (if you have the option) tell it to sort apps by size, and see how big some are: on my phone Google Play Services is using > 700 MB by itself (60MB cache, which can be cleared, the rest being the app itself plus the vast amount of "user data" it stores), my main browser is using a GB (600 MB of which is cache), email apps can be surprisingly thirsty, etc. And remember that if an app stores data in the part of the internal storage that your file browser can see that isn't counted in these totals. So start by looking at the system menu and see what it tells you about how the storage is used, but my guess is that you'll find that one way or another your apps are using a lot more space than you think.
There are apps out there that can give you more detailed information on exactly what is using space. I like DiskUsage for this, which will show how everything but the system partitions is used (you can do nothing about the system storage anyway, so that's irrelevant here).
