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A Hash Index uses a hash table internally to provide extremely fast equality lookups (e.g., WHERE key = value), offering average constant-time (O(1)) access by hashing keys to buckets, but it does not support range queries or sorting.

A Non-Clustered Index is a separate data structure that stores column values and pointers to table rows, speeding up lookups without altering the table's physical order. Multiple non-clustered indexes can exist per table to optimize diverse queries.

A Primary Index is an automatic, unique index created on a table's primary key for fast data retrieval. It ensures quick lookups, enforces uniqueness, and boosts performance in relational databases.

A Unique Index enforces distinct values in a column, preventing duplicates while speeding up queries. It's ideal for fields like email or username, ensuring data accuracy with minimal impact on read performance.

The Leader and Follower pattern improves consistency and availability in distributed systems by electing a single leader to handle all write operations and coordinate replication, while followers act as backups or serve read requests.