What is the difference between development board and emulator?

A development board is the part on a board along with whatever it needs to run (crystal, RAM, etc.) and possibly a few extras such as lights, switches, serial ports, etc.

An emulator plugs into *your* board and acts like the part, but allows you more control (downloading your programs, single-stepping, breakpoints, etc.)

A development board has the hardware on it to start developing your product. You can buy such kits around or make one yourself. Many development boards come with enough chips to talk to a PC through a serial port and have FLASH for your program and RAM. There are already connectors for hooking to a PC and a connector for a power supply. There are extra connectors that bring out just about all the signals so you can hook custom hardware up to it. Some have an area where you can add your own circuits. Some have extras like some LEDs, or an LCD, or some push buttons.

The term emulator has changed a bit. Originally it meant a special hardware device for debugging with a specific processor/microcontroller. You would pull out the CPU/MCU from your developing product, then plug the emulator into where the CPU/MCU was. Inside the emulator was a special version of the CPU/MCU with extra circuitry to enable one to halt, set breakpoints, get/set internal registers, get/set RAM, and upload/download code.

These days, purely software programs that do the same are refered to as emulators although the proper term for it is a simulator. Software "emulators" not only simulate a CPU/MCU but sometimes entire products like videogame consoles.

Homework?

A Development Board is a group of people who know what they're doing, and they make technical decisions.

Emulators do the same thing, except they only act like they know what they're doing.