Shore and sure are easily confused words.
The spell-check application of most word processing software programs would not catch a slip-up of these two words. Spell-check is looking for words that aren’t in its dictionary, and words that resemble words in its dictionary but are possibly spelled wrong. Spell-check isn’t perfect. It doesn’t know and can’t guess what word you wanted or what word you meant, it can only judge the words on the page. If you used words that are all spelled correctly, it gives you a pass anyway. It also doesn’t catch when a word was left out of a sentence.
Autocorrect also isn’t perfect. It suggests words that start with the same letters as you type. It’s trying to save time and effort, but quite often, its suggestions couldn’t be more off base and produces humorous results.
Sure is an adjective, it emphasizes affirmative, definite intent or activity. For example, a sure thing is going to happen, saying I sure will, I sure do means you are going to do what you say you would.
By itself, it can also be an affirmative response, indicating consent or agreement. Based on my personal experience, though, “sure” is not as warmly received as “yes!” or “definitely”, there’s some hesitation being expressed when someone says “sure.” “Sure!” with an exclamation point, or said quickly and enthusiastically, sounds more encouraging to the other party.
Surely is an adverb, and like sure, it indicates intent–something definite, something affirmative. In the sentence “surely you can’t be serious?” the speaker is asking if someone really means what they said, or was it a joke, or said to get an alarmed reaction?
Shore is a noun. It means the coast of a land mass, where the waves break and leave sea creatures and shells behind. Shores can be sandy, shores can be muddy and rocky, shores can be barren or covered in plants.
The following sentence uses both words correctly:
Shirelle was sure that spending summer on the shores of the Seychelles after graduation was her best bet for a great time.
So have you seen shirts or other souvenirs at US beaches that say “it’s a shore thing”? This is a pun of “it’s a sure thing” and that shore sounds like sure. The phrase “it’s a shore thing” could mean “it’s is a beach culture thing, if you don’t love the beach you don’t understand” or “the beach is definitely the place to be”, or a little of both.