Same intention maybe. Same result? Probably not.
Only way to see is to compare, plus Capture One has 4 different methods of Clarity.
So, the same, but different. I doubt there are many adjustments that any two RAW converters will do using the exact same algorithm - each will do it their way because they see that way as "better."
You may prefer one over the other. In general, I prefer nearly all of C1's results over Lightroom (and I assume Photoshop).