Q: How dialysis mode is different from filtration in renal therapy?

Answer: 

Dialysis  means - diffusion-based solute removal
Filtration means -  convection-based solute and water removal

Dialysis is easy to understand as a solute passively diffuses via concentration gradient.

Filtration is an interesting (convection) phenomenon where the frictional forces between water and solutes, results in the  transport of small and middle molecular weight solutes along with water (kind of drag on phenomenon).