Terrain generation won't be noise maps or heightmaps, as those are static terrains
Actually both algorithms can be procedural 3D/2D infinity noises based on world seed value, so they are not static. There are verya large variety of different approaches:
1. If noise values are from 3D noise with height gradient then terrain can form different cliffs and arches (games like Minecraft use this one);
2. If noise values are 2D you will get an infinity heightmap for your terrain (looks like current Java version use some kind of this variant);
3. Combination of 3D and 2D - complex approach when some parts of the terrain defined by 2D noise and some - by 3D (like mountains and valleys).
If islands in the game world will be large than each island probably will have more than one biome, so height values between different biomes will be blended together for smooth transitions (Java version already doing this). I think that islands can probably have at least 2 biomes - the main biome and island shore, bigger islands can probably have more biomes scattered on the land.
There are some more interesting approaches in terrain generation, for example there is a method that can be used to generate infinity heightmap from fixed patterns. This method called stochatic texturing and it was created for textures to make them more realistic, but it also works with heightmaps. Here is the blogpost about texture algorithm
This algorithm can be easily adopted for heightmaps and generate infinity terrain based only on one image. It can be enhanced with adding more images and random rotation and mirroring to samples. Here is my test implementation (without rotation and mirroring, but with noise blending between samples):