booked vs engaged

booked and engaged both are adjectives.

Word	Noun	Adjective	Verb	Adverb
booked	No	Yes	No	No
engaged	No	Yes	No	No

As adjectives, booked and engaged are synonyms defined as:

Other synonyms of booked include set-aside.

booked (adjective)	engaged (adjective)
reserved in advance	built against or attached to a wall
	having services contracted for
	(used of toothed parts or gears) interlocked and interacting
	involved in military hostilities
	(of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line)
	reserved in advance
	having ones attention or mind or energy engaged
	pledged to be married