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.
Banned is the past tense of verb ban. It means to forbid or outlaw an activity or a thing.
Band is a noun. It means a group of people united in a common purpose. Typically, groups of musicians or singers, but it can also refer to thieves.
The following story uses both words correctly:
Benita and her girlfriends were all English Literature majors and musicians. This year, they aimed to start a band called “The Banned Books” and go on tour all summer long.