Pectic enzyme breaks down pectin. Pectin is in most fuit in variable quantities. This enzyme with take away pectic hazes in some fruit wines with high pectin. A pectic haze is a VERY slight haze in a wine that makes an almost clear wine just sort of cloudy, but not enough to prevent you to see through it. So it sort of clarifies the wine. It also serves another purpose, and that is to break down cell walls in the fruit so they release more juice, phenols (flavor and aroma), and color.
Clarifiers help to clear the wine.
Fining agents also help to clear the wine, but they also eliminate very tiny solids that we do not see, and give a wine a "Polish". In kit wines, these are typically one and the same. They help to clarify AND fine the wine.
I find that filtration, puts the final bit of fining on the wine that really makes it look good.