The old fashioned terminology would be "find dog"for Curs or still trailing dogs on cattle or hogs and "strike dog" for open trailing dogs or hounds on whatever. I had never heard of a Cur strike dog until I got to reading on these hog hunting forums, when I first started reading that I thought boy they must have a bunch of open trailing Cur dogs haha.
I always called em find dogs or hog dogs, but after reading this my open cur dogs must be strike dogs