What is the difference between principal neurons and pyramidal cells? I am reading Kandel's "Principals of Neural Sciences". There the book sometimes refers to excitatory neurons as principal cells, and sometimes as pyramidal cells. 

Can anyone tell me the difference? I mean, are there pyramidal neurons which are not projection neurons? And are there projection neurons which are not pyramidal?
Short answer
In the cortex, pyramidal cells and projection neurons can be used interchangeably, as both terms refer to the same cells.  

Background
One way to classify neurons is based on their function. Two functionally distinctive types of neurons have been classified, namely 


Projection neurons, which send an axon out of the structure where their soma is located, and
Intrinsic neurons, which make synapses only within the structure where their soma is located. 


Hence, projection neurons cover some distance, whereas intrinsic neurons act more locally. Projection neurons are also called principal cells, and intrinsic neurons are also called interneurons (Masland, 2004).

In the cortex, projection neurons are pyramidal neurons, and account for approximately 80% of all cortical neurons Han &amp; Šestan, 2013. They often send their axons for long distances, sometimes out of the brain altogether Beckers, 2011. They serve as both the sole output from and the largest input system to the cortex. Interneurons, in contrast, represent approximately 20% of all cortical neurons and form local synaptic connections (intrinsic) that play critical roles in shaping cortical network activity patterns Han &amp; Šestan, 2013. 

In the periphery, the term projection neuron is not used as far as I know. That doesn't mean there aren't neurons that cover great distances in the periphery; in fact, the longest axons in the human body are thought to be situated in the sciatic nerve, which runs from the base of the spinal cord to the big toe of each foot. However these cells are not referred to as projection neurons, but simply as spinal neurons.   

References
- Beckers, Curr Biol (2011); 21(24): PR975
- Han &amp; Šestan, Neuron (2013), 80(5): 1103–05
- Masland, Curr Biol (2004); 14(13): R498