Connotation = something implied in addition to the obvious meaning.

Core =the central core of someone or something ... in a fruit the part containg the seeds as in an apple or pear.
In mining the name of a shift of men working together at the same time.

Inner beauty = within or inside .... as in "Her mouth was too large, her chin too short, her eyes too wide-set, but she was beautiful because her inner beauty shone through.