Yes the C-3 variety of the 1797 half cent comes in three sub-varieties plain edge, lettered edge, and gripped edge.
Yes, I believe the half cent has three varieties. The lettered edge, normal edge, and the reeded edge.
@deacon2828 I never heard of a Gripped Edge. I googled it and found the information really fast. https://www.usacoinbook.com/coins/11/half-cents/liberty-cap/1797-P/gripped-edge/