Nah not really different use cases, just preferences afaik. Some people don't like things going in to their ear canal. I suppose IEMs would also block out more external noise than earphones.

They'll all use the same connector, save perhaps for headphones which sometimes come with a 1/4" connector, rather than the standard 3.5mm

Headphones have a band that goesyour head (or some go around the back of your head) and sit on or over your ears.

Earphones go in your ears, but not into your ear canal. Think of the old school Apple earphones that came with their phones/iPods etc. (on the right in this pic: https://media.wired.com/photos/5932a9a458b0d64bb35d3252/master/w_1280,c_limit/09122012-IPHONE-NEW-EARBUDS-040edit.jpg)

IEMs go in to your ear canal with a little nozzle. These, for exmaple: https://m.media-amazon.com/images/I/61HketTXYcL.jpg The black bit goes in to your ear canal.