engaged vs booked

engaged and booked both are adjectives.

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

As adjectives, engaged and booked are synonyms defined as:

Other synonyms of engaged include set-aside.

engaged (adjective)	booked (adjective)
built against or attached to a wall	reserved in advance
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