Both mean the same...

Bloom and blossom can be use both as nouns and verbs. When use as nouns, bloom means a blossom, whereas blossom means a flower, especially one indicating that a fruit tree is fruiting. When use as verbs, bloom means to cause to blossom. Wherera blossom means to have or open into a blossom. For example Bloom as a noun; The opening of flowers in general; the state of blossoming or of having flowers open. Blossom as a noun: The state or season of producing such flowers. Another Example: Bloom as a noun: A state or time of beauty, freshness, and vigor, an opening to higher perfection analogous to that of buds into blossom. Blossom as a noun: A stage or period development; something lovely that gives rich promise.

In this context, they seem identical to me. There are slight differences between "bloom" and "blossom" when they refer to plants -- I would use "bloom" to describe an individual flower opening up, but either "bloom" or "blossom" could describe a tree growing flowers. "Blossoms" sound smaller to me (the word is often used to describe the little flowers on fruit trees), whereas "blooms" might be fuller and larger, like roses in a bouquet. But if you're describing a person, both words create the same image of someone developing in a flower-like way. My only suggestion is that it would sound a bit better to say "a girl who" rather than "a girl that."

Hi Tomas, i am not a native speaker,for what it is worth About your sentence, change ,, a girl that blossomed into a young lady,, to ,, a girl that grew into a young lady And it will make sense . As far as I know , you cant say : she blossomed into a young lady ,,to mean she became that person To blossom and to bloom means: to become successful or happier For example, you could say: the last time i saw her she was blooming or blossoming as she changed her school and made new friends I hope it helps