An embedded system is basically a computer system that isn't a general computer
- it's embedded inside a product. An embedded processor would just be a procesor used in an embedded system.
A microprocessor is a processor that fits in a few chips, almost always 1 chip these days. Most processors are microprocessors these days: Pentium, SPARC, MIPS, ARM, Z80.
A microcontroller is a microprocessor with I/O devices on it. Most also have ROM (EPROM/FLASH), and RAM as well.
A DSP is a processor specifically tailored for what is needed in Digital Signal Processing. At the least, it usually means there is a Multiply-and-ACcumulate instruction. There's usually more added on. You might want to take a look at the architecture/reference manuals for DSP chips from the likes of TI or Motorola.
FPGA is a Field-Programmable Gate Array. Essentially, a chip filled with gates that you can specify how they are connected. There's usually an EPROM or FLASH, internal or external, that specifies what the connections are. Useful for creating your own low-volume custom chips.