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.
Autocorrect suggests words that start with the same letters. It suggests what word you may want to save time, but quite often, its suggestions couldn’t be more off base and produces humorous results.
Arc is a noun. It means an unbroken portion of the circumference of the circle. Arcs can also mean a object whose shape follows a circle’s circumference, like a rainbow, an archway, or a bridge. It can also mean a path or trajectory that follows an arc pattern.
Ark is a noun. It can refer to a chest or box containing highly valuable objects. It can also mean a a large boat carrying cargo. Arks figure prominently in Judeo-Christian lore: the Ark of the Covenant, and Noah’s Ark. Follow the links for more information on those symbols.
The following story uses both words correctly:
Archie was anxious about all the rain his town was experiencing, was he going to have to build an ark and never return? Even a rainbow’s arc was not an encouraging sign after a storm. The next week’s forecast just promised more of the same: heavy rains they didn’t need.