The incorrect use of em dashes and ellipses is not something that matters a whole lot in the grand scheme of writing. There are more crucial grammatical issues such as direct address commas, apostrophes, and spelling. However, dash/ellipses confusion is a personal pet peeve of mine, and thankfully, the rule is easy enough to remember:
An em dash is the punctuation mark noted by the longer dash. It’s not a hyphen like what you see in this: A two-minute drill. The em dash is longer (—).
Use an em dash (—) for interrupted dialogue, thought, or narrative. Example:
“Why don’t you—” He stopped suddenly and looked behind him.
Use ellipses (…) to denote a small pause, stuttering, or dialogue/narrative that trails off. Here are a few examples:
“And your name is…?” <– In this case the sentence is left hanging or trailing off.
“Are you sure you want to…. you know… go in there?” <– This sentence is using ellipses to show small pauses in dialogue.
What I see writers doing a lot is using ellipses to note interrupted speech, and this simply is not right. I also see em dashes being used to note stuttering in dialogue. While this isn’t a terrible cause for concern, it is important to keep in mind that punctuation symbols mean something! They aren’t just there for you to pick and choose whichever one you want. They all are used for different purposes, and as a writer it’s important to know what those differences are.