engaged vs involved

engaged and involved both are adjectives.

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

engaged (adjective)	involved (adjective)
built against or attached to a wall	connected by participation or association or use
having services contracted for	emotionally involved
(used of toothed parts or gears) interlocked and interacting	highly complex or intricate and occasionally devious
involved in military hostilities	enveloped
(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)	entangled or hindered as if e.g. in mire
reserved in advance
having ones attention or mind or energy engaged
pledged to be married