Unlike the main Pokémon games, there are many different Magikarp patterns in this game. You start off, when catching a Magikarp, having a chance of catching Magikarp in various categories, with different categories having different rarity and a catalogue for you to keep track of all the different Magikarp patterns. The rarer the pattern, typically the larget it can become and the better the ability
As you level up your Magikarp, you may find that it will actually change its pattern to another from the same category. It's not until it reaches the midpoint level that it will grow and register in your list.