The second puzzle is a Nurikabe variation.
Rules for Nurikabe
In this variation there isn't extra rule about the painted squares. They can contain 2x2 area and they don't have to be connected.
Nurikabe has a lot of names. One of them is the Stream Islands (Puzzle Picnic). It is a good name, because the painted squares form a river. Now they are just separeated parts hence I use the Lakes title. (I don't know if the puzzle variation has a regular English title.)
This is a common puzzle type in the Dutch puzzle magazine, Breinbrekers. The size is always huge, but the puzzles are really easy. This puzzle is the counterpoint of that style :)
If you liked this puzzle, you can solve some of my old puzzles from the genre here.