A Beacon Chain validator can also be a shard validator.
Recall, that initially there won't be any shards.
State of Ethereum Protocol #2: The Beacon Chain is a helpful article on these topics and describes that:
validators participate in the protocol by proposing blocks, when chosen to do so, on both the Beacon Chain and, once they have been implemented, ...
Generally, there are beacon chain validators and shard validators.
All beacon chain validators would have the beacon chain.
A beacon chain validator would usually not be able to have all shards (they choose which shards to follow), since the purpose of sharding is so that a single validator doesn't have to validate all transactions in all shards.