What are the other types of database architectures? Oracle, for example has a typical client server architecture, and a memory cache (SGA) with some background processes.

This is one way of designing a database. Are there databases out there which have been designed fundamentally in different ways than this?
Most databases are client/server, although some embedded databases can be used purely like libraries, and share the application's address-space.

The server architecture can vary between databases, and differ from what you described too.  MySQL runs entirely as a single process (with multiple threads).  It does not require any OS shared memory segments or inter-process communication.