I thought OpenCL was supposed to be the "standard"? From the Wikipedia page, it's largely vendor neutral and not that much younger than CUDA (initial release Aug 2009 vs Feb 2007). Maybe some more knowledgeable people can comment why it seems to have been outcompeted by the proprietary CUDA?
OpenCL was definitely supposed to be the standard, but as the sibling suggests, it's just much harder to use than CUDA. Also, it doesn't feel like OpenCL has much of a community around it, documentation doesn't seem great, and just the overall experience is very frustrating. I tried to implement something in OpenCL about 5 years ago, thinking it would be fairly trivial to port a simple compute shader from CUDA, and ended up giving up. Just too difficult.
CUDA has a comparatively nicer user experience. If you would like to understand tacitly and have an nvidia GPU, try writing a simple program using both. (Something highly parallel, like nbody, for example)