slipper vs carpet slipper

slipper and carpet slipper both are nouns.

Word	Noun	Adjective	Verb	Adverb
slipper	Yes	No	No	No
carpet slipper	Yes	No	No	No

As nouns, slipper and carpet slipper are synonyms defined as:

slipper and carpet slipper: low footwear that can be slipped on and off easily; usually worn indoors

slipper (noun)	carpet slipper (noun)
low footwear that can be slipped on and off easily; usually worn indoors	low footwear that can be slipped on and off easily; usually worn indoors
a person who slips or slides because of loss of traction