Sure is an adjective. It modifies nouns or pronouns.

Surely is an adverb. It modifies verbs, adjectives, or adverbs.

Correct: It is a sure thing.
(Thing is a noun. An adjective modifies it.)

Incorrect: It is sure hot outside.
(Hot is an adjective. It should be modified by an adverb.)

Correct: It is surely hot outside.
(Hot is an adjective. An adverb modifies it.)

See also Real or Really?

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