What is the difference between the use of the conditional and the subjunctive?

The conditional is used when, if you meet certain conditions or a fact occurs:

"finiresti prima se ti impegnassi" "sarebbe più bravo se studiasse"

The subjunctive expresses uncertainty and doubt, and is introduced by WHAT. The subjunctive is needed for verbs that indicate willingness, a desire, an expectation, a fear or an opinion:

"sospetto che mi abbia mentito" "temo che si sia offeso"