Usually, but not always. James K. Polk for example conducted one of the most successful wars in our history: the Mexican War. Yet he is among the presidents people are most likely to forget. Polk died almost immediately after his term in office, and the Mexican War is overshadowed by the huge Civil War that occurred only fifteen years later. Woodrow Wilson led a successful American intervention in World War I, but that was overshadowed by an unsatisfactory peace, with the Senate rejecting American involvement in Wilson’s pet project, the League of Nations..
On the other hand Lincoln is remembered for winning the Civil War and ending slavery. His fame however would not burn nearly as bright if our Civil War had merely been a precursor to endless civil wars.
Wars are tricky things when they are being fought, and memories of them are often dependent on events which occur after the wars are done.
Polk was also a man of his word. Before election, he stated he would only serve on term. Despite what would seem an easy re-election, he stepped aside in keeping with the commitment he made. Would that we had more officeholders of like character today.