Well, OP should go into Disk Utility, Debug > Show Every Partition and make sure that's checked, then see what's listed on the HDD/SSD.
Good install will list the OS partition, EFI, Recovery HD, and possibly a second OS partition (if FileVault on).
So, from my understanding, holding option key when booting should list the OS partition, Recovery HD, and any USB attached bootable volumes.
Command-R will drop you into one of the recovery partitions, depending on age of machine. If internet recoverable, and you have the Recovery HD partition, it will boot that (and should be latest OS), otherwise defaults to the internet recovery which defaults to OS system came with. You can install that, then you download/install latest OS.
Can verify the Recovery HD partition version by mounting it in Disk Utility, then select it on desktop/Finder and do a "Get Info". Will tell you OS version it is.
I've got an too old a Mac to see how internet recovery shows things, so, wondering if the system is displaying the internet recovery version number or is it really the Recovery HD partition at 10.9