I think "Bloom" is more directly connected to flowers "Blossom refers to anything showing growth

Both relate, usually, to the flowering of a plant. They can both be used as verbs: the flower blooms in the Spring, the shrub blossomed every year in May. They can both be used as nouns: The cherry tree was full of blossom today, his chrysanthemum bloom was the best in the flower show. Of the two, blossom is probably used most. Blossom can also also be used more generally: after many years as an struggling actor, his career blossomed after he appeared on a popular TV show.