ECC = Error Checking & Correction. Extra chip(s) to help detect and correct errors, usually caused by bits flipped over from cosmic particles.
Registered is an electrical difference, in this case the extra chip(s) isolate/reduce the electrical load on the memory bus, so you can use more DIMMs per channel.
It is possible to have DIMMs that are ECC and unbuffered (not registered), and you can also have RAM that is registered and not ECC.
In order to make use of either, your board's BIOS and chipset (or else memory controller) must support these. Also, it's sometimes possible to use ECC RAM in a non-ECC board, as the board will simply ignore the unknown feature. However, registered RAM can only be used in boards supporting that feature.