Hi Hingol,

It is all just part of the whole Solunar theory. Sun - moon - tide etc.

If you compare what Fishing Reminder says against what the locals there say, I think they might be pretty close together. The difference is that your locals are only looking at moon to tide. Where as Fishing Reminder takes all the factors to predict the best fishing times.

There is plenty of information about moon affect on tides and fishing. But when you start combining sun, moon and barometric pressure etc, etc you start to see some really interesting stuff.

Maybe they mean the tide level difference?
The closer the moon is to earth, the bigger will be the gravitation. 
This causes bigger tides and and a bigger difference between low and high tide.
This would then also cause the tides to run in and out faster I assume.
And those stronger currents could bring in some predator fish.