Why get a separate amp and preamp when you can get a receiver that includes both functions? The short answer is that you can get better sound and more system-building flexibility.
Integrated amplifiers
An integrated amplifier is two components in one — a power amp that drives your speakers and a preamplifier for your music source components. The preamp lets you select your sources and control the volume.
Power amplifiers
Hi-fi stereo amps are for high-performance stereo music systems. They can be used in surround sound systems, though multi-channel amps might make more sense for that purpose.
Monoblock amps have just one channel. Some models are designed to drive a passive subwoofer. Others are meant for audiophiles who like to use a separate amp for each channel of their system.
Multi-channel home theater amps are the companions for surround sound preamp/processors. You'll need at least five channels for a surround system. You can choose a powerful 3-channel amp to drive the front left, right, and center channels. Your surround speakers, which may require less power, can have their own 2-channel amp. If you want to keep things simple, get one amp with enough channels to drive all of your speakers.
Stereo preamps
A stereo preamp includes connections for your source components, as well as tone, balance, and volume controls. There's a switch to select the component you want to play. Some models include a built-in network music player.
Surround sound preamp/processors
Think of a surround sound preamp/processor as a home theater receiver without the built-in amplifier. It does the video processing, surround sound decoding, input switching, and audio signal processing. Most models come with built-in room correction software that helps fine-tune the sound.
Multi-zone amplifiers
Multi-zone amps are building blocks for a multi-room system. You get at least two channels of power. Some models include as many as 16 channels. Many models include connectors for remote control, power triggers, and infrared signal transmission.