They approached their idea of victory in two very different ways. Davis's idea of victory was for the Confederacy to survive the war and not falling to the Union. His goal was not to have the Union fall to the Confederacy. Lincoln's view of victory was instead of restoring the Union; he needed the Confederacy to fall in order to be victorious.
As far as warfare is concerned, for the most part Davis fought a dominantly defensive war with very few exceptions. Lincoln on the other hand fought a very offensive war. Logically, the north should have been able to easily subdue the south due to vast resources (both material and manpower). However, this was not the case since the south had all the truly military (as opposed to political) generals. So it would be a long war until Lincoln put truly military generals -- such as Grant and Sherman -- into control.
