3 Tier Architecture

Two –tier Architecture: A two-tier architecture is where a client talks directly to a server with no intervening server. It is typically used in small environments. Here you can add more users to the server. This approach will usually result in an ineffective system, as the server becomes overwhelmed to properly scale the users.

Eg. Oracle Products SQL*NET is the middleware between the client/server systems.

Three – tier Architecture: A three – tier architecture introduces a server or an agent between the client and server. The role of the agent is manifolds. It can provide translation services (as in adapting a legacy application on a mainframe to a client/server environment), metering services (as in acting as a transaction monitor to limit the number of simultaneous requests to a given server), or intelligent agent services (as in mapping a request to a number of different servers, collating the results and returning a single response to the client.

E.g. The Application Programming Interface (API) like ODBC is the middleware between the client and server development in this architecture.
The primary advantage of using API in client application is that the resulting application can then use any backend database servers rather than specific server.
The disadvantage of using API is the "Least common denominators" of all tools and database servers that support the standard. Therefore, when you develop a client application, you might not be able to take advantage of all the unique and special features that any one database servers offers.