Multi-choice question: Same meaning?
The exponential map of a nilpotent Lie algebra is a diffeomorphism between the Lie algebra and the unique associated connected , simply-connected Lie group .
The unique map of an exponential Lie - Algebra is a diffeomorphism between the Lie - Algebra and the nilpotent - associated , simply associated lie group .

OPT: (A). no; (B). yes;
(A).