From the beginning of Harvest Moon series, fishing is one of the many activities you can do to pass time and earn money. As the series progressed, little has changed from the fishing mechanics aside from change in controls.
In Rune Factory 3, you can now actually see the fish in the water (or in the sand). All you have to do is cast your rod and wait for the fish to bite the bait.
In Harvest Moon Grand Bazaar, this feature is carried over but with some changes. In this game, you're only allowed to fish on predefined spots. The fishes are also arranged in an obvious layer that puts the smallest fish nearest the pier and bigger ones farther away. You need a better fishing rod to reach those big fishes.
In the end, it is real good for these games to adopt each others features. Now if harvest moon has animated cutscenes, more voice acting and deeper storyline...