Vain and vane 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.
Autocorrect suggests words that start with the same letters. It’s suggesting what word you may want to save time, but quite often, its suggestions are pretty off base. They don’t help you out, but they do make you laugh.
Vain is an adjective. It describes someone obsessed with a refined appearance at all times. Vanity, the noun form, is the quality of being obsessed with one’s own image.
Vane is a noun. It is a metal blade or set of blades that are moved naturally or artificially by air or water. For example, a weather vane is metal device on a roof’s apex that is indicates of wind speed and direction. In a figurative or metaphorical sense, someone who is vane is fickle, or always changing and hard to please.
The following story uses both words correctly:
Vance had pink hair and unique expressive fashion sense. His family accused him of being vane and hard to get along with. His classmates felt he was shallow and vain, that he was all about appearances. Vance felt he was bringing much needed color and excitement to his otherwise predictable hometown of Venango.