vs 

QUICK ANSWER
"No, thanks" is an interjection which is often translated as "no, gracias", and "I'm fine" is a phrase which is often translated as "estoy bien". Learn more about the difference between "no, thanks" and "I'm fine" below.
no, thanks(
no
 
thahngks
)
An interjection is a short utterance that expresses emotion, hesitation, or protest (e.g., Wow!).
interjection
a. no, gracias
Do you want to finish the garlic bread? - No, thanks.¿Quieres comer lo que queda del pan de ajo? - No, gracias.
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I'm fine(
aym
 
fayn
)
A phrase is a group of words commonly used together (e.g., once upon a time).
phrase
a. estoy bien
How are you, Laura? - I'm fine.¿Cómo estás, Laura? - Estoy bien.
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