Both words have almost similar meaning.
Aplomb means complete and confident composure or self-assurance. In general it is used to define a situation handled with confidence and style
Sangfroid means self-possession or imperturbability especially under strain (Derived from Latin words sanguis “blood” and “frigidus” “cold”)
She played several roles with equal aplomb
He displayed remarkable sangfroid when everyone else was panicking during the crisis.
The gambler seemed to take both his wins and his losses with remarkable sangfroid
He conducted the meeting with his usual aplomb