There are plenty of fish to catch around the world and they come in different sizes as well. When the fish is still small, you can keep them within a nursing zone that will keep them safe and allowing them to grow over time. When the fish has grown big enough, you can let it swim in the water around your farm and they will not get lost or escape like smaller fishes.
Any fish above the size of "S"(Small) can be left outside the nursing zone as they are more independent and do not need as much care as smaller fishes. A point to be taken is that not all fish can grow up to "L" size so some might stop growing after hitting "M" size or stay as "S" size forever.
List of Fish
Not yet implemented in the game: