Look! It's a VIC-20 dipped in tar! It's a C64 that's been char-grilled! No... it's a completely different machine from both of those.
The Commodore 16 is a member of Commodore's ill-fated 264 series. It has an updated graphics controller, a new improved version of BASIC, and it's quite incompatible with the Commodore 64. Secret Weapons of Commodore! mentions several machines in this series, and they make interesting reading, but the only two 264s that made it into the mass market in meaningful quantities were the C16 and the Plus/4.
Besides not being compatible with the C64/C128 (at the time, one of the most popular machines on the shelves), Commodore also changed the joystick, cassette and cartridge ports on the 264 series, and eliminated the user port. This seems insane - even beyond the normal Commodore level of bizarre and/or stupid decisions. The user port wasn't a very big deal - it was mostly used for modems and proprietary printer interfaces - but why did they have to change the other ports? The only factor that makes some sense is that the C16's PCB is much smaller than that of its predecessors (thanks to TED). Perhaps Commodore didn't want to waste the materials making the board long enough to stretch across the entire back of the machine, and so they had to use smaller connectors.
My unit is a standard North American market version, bundled with a tutorial cartridge similar in concept to the "Apple Presents Apple" disk bundled with the Apple II series. As you can see from the box photos below, it is billed as "the world's learning machine"; perhaps Commodore aimed it at teaching computer literacy? I have read that the C16 was, like the Plus/4, aimed at business applications, but I find that very hard to believe.
I bought my C16 purely because I wanted one way back in the 1980s when they came out. In Australia, the C16 was sold from its introduction date in a package with a joystick, the Jack Attack cartridge, and a blue Commodore-badged sports bag big enough to hold the computer, for AUD$129.
Pricing on collectible C16s is very variable. I paid about US$20 for mine, but I have seen them go as high as $170 recently. Bide your time; this machine isn't fantastically useful and it's not worth spending a lot on unless you're a serious historical collector.