This study examines two essential characteristics of permutations within algebraic frameworks. The initial emphasis is on the full differential uniformity of permutations within a finite commutative ring possessing unity. We generalize the permutation results examined by Gupta, Mishra, and Gaur [10] in 2021 about Zn to encompass broader finite commutative rings. Expanding upon the research conducted by Canteaut, Duval, and Leurent, [3] in 2015 about differential uniformity bounds for functions derived from Feistel and Misty architectures, we introduce novel bounds for functions formulated using Lai- Massey structures.