handling charge vs handling cost

handling charge and handling cost both are nouns.

Word	Noun	Adjective	Verb	Adverb
handling charge	Yes	No	No	No
handling cost	Yes	No	No	No

As nouns, handling charge and handling cost are synonyms defined as:

handling charge and handling cost: the cost of handling (especially the cost of packaging and mailing an order)

handling charge (noun)	handling cost (noun)
the cost of handling (especially the cost of packaging and mailing an order)	the cost of handling (especially the cost of packaging and mailing an order)