What is the pronouncing difference between /æ/ and /e/ in US English?

For Minnesota and other cities around the Great Lakes, you're looking at the https://en.wikipedia.org/wiki/Northern_Cities_Vowel_Shift /ae/ raises to /ɛə/ or even /ɪə/; in response, in some dialects, /ɛ/ is backing and lowering to /ɐ/. Some good examples of a really advanced variety http://www.pbs.org/speak/ahead/change/vowelpower/vowel.html and more explanation of what's going on http://www.pbs.org/speak/ahead/change/changin/summary/

Have you already been to the http://accent.gmu.edu/? Lots of samples there of the same passage of text. http://accent.gmu.edu/browse_language.php?function=detail&speakerid=62 http://accent.gmu.edu/browse_language.php?function=detail&speakerid=98 etc.

Grew up in New York City, parents were not native New Yorkers (so minimal "New Yawk" accent), have lived all over the midwest in adulthood and sound afaik like a midwesterner. Bread rhymes with dead, Fred and Fed. I say it with my lips closer together and held wider. My tongue is in the center of my mouth. Brad rhymes with lad, fad, and gonad. My jaw drops more and my tongue sinks to the bottom of my mouth. The above seem to be true in Cleveland, Ohio, where I currently live, as well as in St. Louis, Missouri and Southeastern Michigan. I spend a lot of time in Milwaukee and have no trouble understanding or making myself understood.

Some accents just don't have all the vowel sounds that other accents have. To the extent that speakers of that accent don't even know those other sounds exist and can't hear them. This is my experience as someone from the Northeast who moved to the mid-west. Southern and mid-western accents don't distinguish between marry/merry/Mary, pin/pen, etc. They just don't do it. For example my coworker from the South said something like "He's taking the one at the end" and I responded "The one at the inn? What inn?" You need the context to know what word they're using no matter how fluent you are. I have personally never noticed this bad/bed man/men thing but I would put it down to the same phenomenon.

This has something to do with the https://en.wikipedia.org/wiki/Northern_Cities_Vowel_Shift.

The physical shape of the vowel is different. For the first words, my lips move vertically. For the second, my lips move horizontally, like a closed mouth smile movement, but obviously not closed mouth.

http://ask.metafilter.com/285183/What-is-the-pronouncing-difference-between--and-e-in-US-English#4131850 Maudlin, these two tools are too complicated for me to understand. Thanks. Click this http://accent.gmu.edu/browse_maps/namerica.php; click a flag on the map; when the new page loads, you should see a little sound bar player thing near the top, and the text of the speech written below. Hit the play button. Everyone reads the same text, and you can listen to e.g. someone from Iowa read the same thing as someone from New Orleans, as in the links maudlin posted. (If you don't see the little player bar, try a different browser.)

Native Iowan here, and chesty_a_arthur's description is spot-on for how I'd describe pronunciation. I'm not familiar with the Michigander accent, but I'd agree that any Ian who is having his name misheard as Ann is not enunciating clearly -- Ian is two syllables. The Minneapolis/St. Paul region of Minnesota definitely shares its accent with most of Iowa/Nebraska, but the stereotypical Minnesota accent is the one heard in movies like Fargo and tends to elongate words with "ou" as "oo." Words ending in "d" or "t' will have that letter audible. The Midwestern/"broadcaster" accent seems like it stretches out vowels compared to east coast accents.

So, I speak rural Southern Ontario English and know plenty of people who speak the related Michigander English and I think this example is faulty. Ann and Ian don't sound the same because Ian has an unmistakable dipthong. Instead, Ann and Enn sound almost indistinguishable. The story would make a lot more sense if the character was a girl named Elle (who everyone thought was named Al). The /ae/ in "Ann" is often dipthongized (with a schwa off-glide, as I noted above) as a result of the NCVS, so it would sound like "Ian"; this mishearing is something I have heard of happening. So, that's one thing you could focus on, OP-- the /ae/ in the midwest will have two vowel sounds in it; the /e/ will be more monopthongal (one sound), unless the speaker has a highly advanced variety.