Most baby plants are called "seedlings". However, the term "sapling" also often applies to baby trees.
When seeds absorb water, they begin to germinate. The first part of the plant to emerge from the seed is the root, which absorbs additional water and nutrients from the soil as the process continues. Soon after the root emerges, the seed sends up a shoot, which pops up above the soil to collect sunlight and enables the plant to continue to grow into a seedling.
Seeds need adequate amounts of water in order to germinate. Soil condition is not overly important in the sprouting stages, but becomes vital soon after the root and shoot emerge. Seedlings need rich soil, plenty of water and sunlight in order to thrive and grow into full-sized plants.