Shared nothing typically refers to hardware, though it could also be used when describing an SOA architecture.
From a hardware perspective, a "shared nothing" Oracle database simply means a machine using local disks, memory, etc.
Oracle RAC (real application clusters) is a shared disk architecture, but not shared memory. Horizontal scaling is then achieved by adding more machines to the cluster.
When talking in SOA terms, "shared nothing" means that each service has a corresponding database which is only accessed by that service. So the ACCOUNTS service accesses the ACCOUNTS_DB, ORDERS service the ORDERS_DB and so on. These databases could be shared nothing from a hardware perspective as well, or use RAC.
Ensuring consistency of data and references which would normally be handled using foreign keys becomes a challenge in SOA shared nothing databases.
Sharding typically refers to partitioning managed at the application level, rather than within the database. For example, you could partition accounts by email address and direct customers with address starting A-C to ACCOUNTS_DB01, D-F ACCOUNT_DB02 and so on. The shard mapping could be a simple range like this, a function on the input or a lookup database stating which database is stored in. The databases would be "hardware shared nothing" in this case as the idea is you use relatively cheap machines which are easily added and replaced.
You could shard your databases at the application level and still have Oracle partitioning at the table level within the database itself. So you could shard your ORDERS database by customer, then partition the orders table by order date as well inside the database.
The downside to both meanings of shared nothing comes if you frequently run queries that have to access several databases. In these cases your joins will be pushed into the application layer rather than the DB layer so are likely to be slower. Good governance is necessary to ensure this doesn't happen.