I am new to Godot/game engines in general and following my first tutorial. What could cause the difference between the tutorial (left) and my (right) map difference.
I have went through the tutorial again and ended with the same result. Is there a setting he may have changed previously and forgot to include it in the tutorial.
I also tried searching for the issue, but I am not sure it was effect due to a lack of knowledge to explain it well without a picture.
Looking at your comparison, I believe the difference is layers rather than a setting. That dark band between your grass and the water is the grass tile’s transparent edge with nothing behind it.
Grass edge tiles in these tilesets have partial transparency so the water can show through underneath. In the tutorial the water is on its own TileMapLayer below the grass layer, so the grass overlaps water everywhere. If you paint both on the same layer, placing a grass tile replaces the water tile in that cell, and the transparent part of the grass edge shows the background instead of water.
To check, look at your scene tree. The tutorial project likely has two TileMapLayer nodes, something like Water and Grass. If you only have one, add a second layer, fill the lower one with water under the whole island (including under the grass), and paint the grass on the layer above. The dark band should turn into water like the tutorial.
If you already have two layers and it still looks like this, can you post a screenshot of your scene tree and the tile painting view? That would help narrow it down.