A good way to remember the difference between the two hormones is to understand their names and work through the logic behind their mechanisms of action.
ADH stands for antidiuretic hormone; a diuretic is something that increases urinary output, so ADH has to be a compound that decreases urinary output by conserving water. The only way to increase water conservation in the nephron without affecting secretion of anything else is to increase water reabsorption; thus, ADH must act on a part of the nephron that is normally impermeable to water, the distal tubules and collecting ducts. If you can remember that ADH is secreted by the posterior pituitary, you can deduce more about its mechanism of action. Hormones secreted by the posterior pituitary are synthesized in the hypothalamus, packaged in vesicles, and transported down axons that terminate in the posterior pituitary. Because they are packaged in vesicles to be secreted on demand, posterior pituitary hormones like ADH cannot be lipid soluble. Thus, ADH has to bind to receptors on the basolateral membranes of cells of the distal tubules and collecting ducts in order to make those cells' apical membranes more permeable to water. (When ADH binds to V2 receptors on the basolateral membrane, the cell inserts aquaporins into its apical membrane.)
Aldosterone is a steroid hormone (like testosterone or progesterone). Steroid hormones work by altering gene transciption, since they can cross lipid membranes and bind to intracellular receptors. Aldosterone, among other things, upregulates transcription of the Na+/K+ pump gene. Since they control the ECF/ICF concentrations of Na+ and K+, Na+/K+ pumps will be found on the basolateral membranes of cells of the nephron (Apical membranes don't touch the ECF.). What would a larger number of Na+/K+ pumps do? It would shift Na+ from the cell into the blood across the basolateral membrane; as we know, the concentration of Na+ inside a cell usually stays constant, so to compensate Na+ will diffuse across the apical membrane from the filtrate into the cell, effecting a net removal of Na+ from the filtrate into the blood. By the same reasoning, a net secretion of K+ from the blood into the filtrate is effected. Conservation of Na+ is aldosterone's primary function.
