We explore the diffusion and relaxation dynamics of a single ring polymer strongly adsorbed on rough surfaces with different roughnesses by means of molecular dynamics simulations. Our simulations demonstrate that on rough surfaces the intrachain topological constraint deriving from the closed architecture induces the inconsistency of diffusion and relaxation of ring polymers. When the lateral chain size is larger than the obstacle distance (2R(g parallel to,r) > d), the ring closure induces the polymers to anchor on a single obstacle and dramatically reduces their diffusivity, where R-g parallel to,R-r and d are the lateral components of the mean-square radius of gyration and the obstacle distance, respectively. However, the single obstacle anchoring has no effect on the relaxation of ring polymers, which implies a deviation between the diffusion and the relaxation. With the lateral chain size beyond twice of the obstacle distance (R-g parallel to,R-r > d), the ring polymers are totally confined in the array of obstacles and can only diffuse through hopping over the obstacles, resulting in an exponential reduction of their diffusion coefficient. However, the relaxation of ring polymers mainly depends on their rotating reptation and satisfies the reptation-like dynamics, which means that the diffusion and the relaxation are nearly irrelevant. This inconsistency between the diffusion and relaxation is a unique property of adsorbed ring polymers, which would be meaningful to understand the physical nature of polymers with ring closure and significant to develop the corresponding applications.