Germination is the process of seeds developing into new plants. A common example that you may find is a seedling sprouting from a seed from the time it was planted. For seeds to germinate, necessary conditions must be met including suitable temperature, water (moisture), air and more importantly, adequate amount of sunlight.
On the other hand, vegetative propagation refers to the process of growing new plants using its vegetative parts such as roots, stems, and leaves. Vegetative propagation can proceed naturally or with human interception, often referred to as artificial methods. Plants that undergo natural vegetative propagation include bulbs, cloves, corms, runners, etc. whereas artificial methods include cutting, layering, and application of techniques such as budding and grafting to produce desirable duplicates.