誇張する・ こちょうする: exaggerate in a fairly literal way: You saw one celebrity, but claim that you saw 6.

大げさな: おおげさな: To exaggerate in your attitude, without actually bending the facts. For instance, you get a little scratch but act like you need to go to the hospital. 大げさalso means, 'to talk in a grandiose, pompous way.'