They technically are both "hardware" raids, but what really sets the two apart? Wouldn't on-board raid basically be a software raid since they share the same processor.
What a RAID card brings to the table...
More processing power. Dedicated chips to handle the calculation of things such as parity. Hardware that is not a shared resource. Dedicated memory. Optionally, write-back cache with it's own battery module (to preserve the cache in the event of a power failure).
On-board RAID CAN be fully dedicated RAID, just on the motherboard. I'd venture to say that most of this time, this is actually a scaled down solution, sometimes called "software-assisted RAID." It's a partial solution, but still relies on shared system resources.
Finally, to answer your question -- "Wouldn't on-board raid basically be a software raid since they share the same processor": It depends on the implementation. Some motherboards are going to come with more dedicated RAID resources than others. Undoubtedly, some effectively be a software solution because they are offloading so much of the work to the rest of the system, effectively relying mostly on the OS. It's entirely possible that the actual OS implementation of mirroring may do a BETTER job than solutions like this. Other on-board implementations may provide a full RAID chipset, with dedicated RAM for the on-board RAID.