The disciplines are very similar, and it is very easy for a climber to make the transition because they already have experience with ropes, but there are a lot of canyoneering specific skills and gadgets that are different from climbing. If I were to campare the two by their differences, I'd say that rock climbing requires more strength, and canyoneering requires more wisdom.
First of all, when canyoneering you obviously spend a lot more time on your ropes, so the first essential skill you need to learn how to do is how to make anchors for descending while pulling your ropes. It is incredibly easy to get a rope stuck in a canyon, and when it happens it could mean big trouble, chances are you'll have to cut your rope and hope there's enough left over to make it the rest of the way out if you don't have a second rope (which you probably should).
Canyoning descenders are different too, they offer many different levels of friction, and are easy to tie off if you need to stop and go hands free.
Stirling Ropes ATS
One thing about canyons, is that they all have one thing in common: water. Every canyon is cut out of the earth by flowing water, and the best canyoneering is in the canyons that have flowing water. Descending down waterfalls, sliding down natural waterslides, cliff jumping into deep pools and swimming through long winding meanders with tall cliff faces on either side of you in a place that receives fewer visits than most others are the big attraction for serious canyoneers.
If you're planning on visiting a wet canyon, then you need a few more things, namely: a wetsuit. Then you'll want to get a seat protector for your harness to protect your wetsuit while sliding on your bum:
There are also special shoes for canyoning that are insulated with neoprene and have super sticky rubber for wet rocks, canyoning helmets that don't hold water, PVC bags for your rope and gear, treatments for your ropes to make them float. There's a lot...
Canyoneering is it's own sport, but it falls under the family of greater alpinism, so naturally being a climber will make it easier to transition into it, but being a climber isn't enough if you want to do the fun wet canyons, you also need to be a navigator, a swimmer, a cliff jumper, and in some cases a diver.