Are SQL Server statistics stored in database or buffer pool?
The buffer pool is a cache of the database. There is never an 'or', things that are in the buffer pool are also in the database, always. And anything read from the database must be, even temporarily, present in the buffer pool. 

As for the question: statistics are in the database so a backup/restore will preserve the statistics. 

Note though that preserving statistics is not a guarantee to plan reproducibility. Other factors influence plan generation, like number of CPUs and amount of RAM.