They are completely different words. Neither of them is basic vocabulary. 1) "Aren't you going to rehearse your presentation?" "No, I know the subject. I'm prepared enough." "I think you are too complacent." 2) "He thinks he's wonderful. He thinks he's the smartest person in the world, the most handsome person in the world, and the best dancer in the world. He's the most conceited person I've ever met."

Complacent: satisfied with how things are and not wanting to change them The strong economy has made people complacent. Conceited: having or showing too much pride in your own worth or goodness a brilliant but conceited [=vain] musician

As adjectives the difference between complacent and conceited. is that complacent is uncritically satisfied with oneself or one's achievements; smug while conceited is having an excessively favorable opinion of one's abilities, appearance, etc; vain and egotistical.

conceited = vain. Someone who is conceited thinks very highly of themselves. They like themselves a lot. It is a negative thing to be conceited. Someone who is complacent is lazy. They believe they are good enough and don't try to do any better. This can often result in problems for them later.