baby bed vs carrycot

baby bed and carrycot both are nouns.

Word	Noun	Adjective	Verb	Adverb
baby bed	Yes	No	No	No
carrycot	Yes	No	No	No

As nouns, carrycot is a hyponym of baby bed; that is, carrycot is a word with a more specific, narrower meaning than baby bed:

baby bed: a small bed for babies; enclosed by sides to prevent the baby from falling
carrycot: box-shaped baby bed with handles (for a baby to sleep in while being carried)

Other hyponyms of baby bed include bassinet, cradle, cot, crib.

baby bed (noun)	carrycot (noun)
a small bed for babies; enclosed by sides to prevent the baby from falling	box-shaped baby bed with handles (for a baby to sleep in while being carried)