봄(bom)
The season after winter when the weather starts to warm up
When to use
Season start, Flower blooming, Sprouting and growth
The nuance
봄 (spring) covers March to May; it signifies blooming flowers and new growth, used in contexts of beginning, renewal, and growth.
가을(ga-eul, gaeul)
The season after summer when the weather starts to cool down
When to use
Season end, Falling leaves, Harvest and change
The nuance
가을 (autumn) spans September to November; it features falling leaves and harvest, used in contexts of endings, change, and maturity.