"Bloom" infers that the flower is at its fullest, brightest stage.
"Blossom" can be a verb describing the process of a bud slowly opening up into a bloom, or it can be a noun which describes a flower which is in the early stages of "opening" up into full bloom.
If you like blooming flowers, it means you appreciate the beauty of flowers at their brightest and best. After they bloom, they will slowly begin to wilt and die.
If you like blossoming flowers, you enjoy watching the process of buds slowly opening and spreading their petals, eventually reaching full bloom.
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