I think I understand sharding to be putting back your sliced up data (the shards) into an easy to deal with aggregate that makes sense in the context. Is this correct?
Sharding does more than just horizontal partitioning. According to the wikipedia article,
Horizontal partitioning splits one or more tables by row, usually within a single instance of a schema and a database server. It may offer an advantage by reducing index size (and thus search effort) provided that there is some obvious, robust, implicit way to identify in which partition a particular row will be found, without first needing to search the index, e.g., the classic example of the 'CustomersEast' and 'CustomersWest' tables, where their zip code already indicates where they will be found.
Sharding goes beyond this: it partitions the problematic table(s) in the same way, but it does this across potentially multiple instances of the schema. The obvious advantage would be that search load for the large partitioned table can now be split across multiple servers (logical or physical), not just multiple indexes on the same logical server.
Also,
Splitting shards across multiple isolated instances requires more than simple horizontal partitioning. The hoped-for gains in efficiency would be lost, if querying the database required both instances to be queried, just to retrieve a simple dimension table. Beyond partitioning, sharding thus splits large partitionable tables across the servers, while smaller tables are replicated as complete units