Unable to install OS X, cmd+R opening internet recovery instead of usual recovery
Your model Mac was shipped with Yosemite (OS X 10.10) installed. The tags you placed on the question suggest you have upgraded to El Capitan (OS X 10.11). There is the possibility you could have erased the Recovery partition by using the Disk Utility if you had Yosemite installed. Evidently, this would be much harder (or perhaps impossible) to do if El Capitan was installed. Also, I do not know if you were using Core Storage and if so, how this would effect the ability to erase the Recovery partition.

Evidentially, you can now only boot using OS X Internet Recovery. You can use Internet Recovery to install the version of OS X that came with your machine. From this, you can go to the App Store and download and install newer versions of OS X.

An alternative would be to use another Mac to download OS X. You can then transfer the download to a USB drive. You then use the USB drive to install OS X on your Mac. The instructions are given the Apple web site: Create a bootable installer for OS X.