To answer your first query.. Blockchain is the concept and hyperledger fabric is merely an enterprise based blockchain platform for private solutions.
Hyperledger fabric is specification for how trusted network should work,
Hyperledger is a community supported by different vendors. Some of these
Fabric is given by IBM
Intel gave Sawtooth Lake
Iroha was given by Soramitsu.
Difference between Blockchain and hyperledger
While Blockchain is a concept which can be implemented in many ways. It is basically a technology that stores data, on the other hand hyperledger uses blockchain as its database with another logic which is platform or framework dependent.
Answering your another question: hyperledger transactions are stored in the blockchain nodes.
Does every peer has a copy of growing transactions? Many peers have a copy of transaction ledger. For strong network, blockchain needs atleast 50% of the nodes to approve the transactions.
Transaction database: fabric uses Leveldb as a world state database, but this can be changed CouchDB for more complex queries.