>>35665535The Lake Trio have actual importance to the plot and help to progress it, alongside having much more significant lore and connection to the Creation Trio. They're literally called the "Lake Gods" in Japanese.
The Genies just exist, you can only catch two of the three depending on the version of the game you're playing and they have a much less significant lore.
You can't obtain their other forms without playing the shitty Dream Radar thing iirc.