The two important high-availability features from SQL Server 2008 R2 are failover clustering and database mirroring. Both of these features are fundamentally different in terms of implementation, having instance level availability for failover clustering and database level availability for database mirroring.
In terms of architecture, both have the same concept of quorum, heartbeat, and witness server to support automatic (for database mirroring it depends on the implementation mode) and manual failover. In terms of connectivity, during a failure, failover clustering does not require any changes in the application connection string. However, for database mirroring, the application may require changes to the connection string, to force a reconnection after a failover. In such cases, ensure to cache the partner information to update the connection string, or retry connectivity when the first connection attempt fails.
However, as a...