Amber Basics
Amber appears as Amber Ore, 
Amber Block, 
Amber Gem, Amber Grass, Amber Moss, Amber Moss Path, and Amber Root Seed. Mine Amber Ore in Amber Grass biomes to get Amber Gems. Place Amber Blocks for decoration or storage. Use Amber Root Seeds on Amber Moss to grow more Amber Grass, giving you a renewable source of the moss and grass blocks for building.
Aurora Crystal Basics
Aurora Crystal and Aurora Crystal Shards come from Aurora Crystal formations in the colder, darker End biomes. Break the crystal blocks to collect shards. Shards are the crafting ingredient for Aurora Crystal blocks and for several light-emitting or decorative recipes. 
Ancient Emerald Ice is found in similar cold biomes and pairs well with Aurora Crystal in builds.
A Simple Farm Loop
1. Find an Amber Grass biome and mark it.
2. Harvest Amber Ore and take Amber Root Seeds home.
3. Plant seeds on Amber Moss in your base to grow Amber Grass indefinitely.
4. Separately, locate an Aurora Crystal cave and mine a stack of shards.
5. Store shards in a chest near your crafting area — you will use them often.
Both resources are non-renewable from ore in the strict sense, so replant Amber and revisit crystal caves rather than stripping them completely.