Here are the definitions of the three words "Felting" "Fulling" and "Boiling".

Felting is in essence the characteristic nature of animal hair, wool, fur etc. by using heat to open the scales of the fibers and then agitation of some kind to shrink and compact the fibers depending on the use of the finished product.

all three of these processes use this same charactaristic of "Felting".

Felt - The word is usually said to come from the Old High German word 'filz' used in the 12th century.
Felt is the name for the fabric itself.
This is where animal fibers that have possibly been dyed but not spun or woven are treated with heat to open the scales of the 'hairs' and then agitated, rolled, hammered or otherwise compressed together. This forms the material we know of as felt.
This is how quality Stetson beaver Felt hats are made. A hard, dense, Felt hat will hold water and retain it's shape for years. (it is also a similar process to making dreadlocks) Mongolian Yurts are made of Felt.

Fulling - From the Medieval Latin word 'fullare' meaning to walk or trample.
This is a process that usually starts with the knit or woven articles of clothing.
Fulling is a way of cleaning the item along with felting it. In the Middle Ages Fulling was done in large vats of hot urine and literally walked on. Then "Fullers Earth" a chalky, fine dust was added to absorb the grease and oils. This produced a garment that has very little of the oil, grease and dirt found in natural wool without removing all the Lanolin. Fulling produces a garment that is very light, very soft and not itchy. Old style wool underwear was Fulled as were some Leine. Linsey/Woolsey cloth was often Fulled.

Boiling - This process is most famous from the Alpine region of Austria and Switzerland but is also widely used in S. America.
Boiled Wool is the name for the fabric.
Instead of loose fibers for Felt or made up garments like Fulling, Boiling is done on large quantities of knit or woven fabric before it is fashioned into garments. This produces a fabric that is of consistent thickness and finish. Tyrolian jackets are made from Boiled fabrics. I remember a pair of boots made from Boiled Wool that my Grandfather had. In the snow they were better than any leather or plastic boots available. Hudson's Bay Blankets used to be of the finest Boiled Wool and they still claim to use it but it's not the same now.