Definitions exist. People either interpret or make up their own stuff. For real, semi-formal is a tux for men (and nowadays, a nice black suit, white shirt and tie might work) and a dressy cocktail or floor length dress for women. Formal is white tie and ball gowns.
Ask the hosts. I’ve been to parties where semi formal meant real hot dog buns instead of sliced white bread.
Where I live, semi-formal means a shirt with buttons. Formal means that the shirt is tucked in.
I once showed up at a friend’s wedding in a suit and tie (I was coming from some business event). The groom chastised me for being better dressed than he was.
Dark suit, white shirt and non-cartoon character or light up necktie for men.
Dressy dress but not floor length for the ladies.
This brings back memories of my 8th grade graduation dance in 1968. It also was advertised as semi formal. I showed up in a pink, lacy, knee-length dress - to me, formal was a floor-length gown. Others showed up in shorts and sandals. Yeah, I felt a little out of place.
As a 50-something myself, I’d say suit and tie/nice dress or dressy pants and top. At least, that’s what I’d wear in a similar situation.
Are these the types of people you could see having a formal-meaning-tuxedo type wedding? If so, then semi-formal means suits for men, and cocktail dress for women. Nice flat shoes are fine. Most women who don’t have medical issues will be in heels.
If these are pretty casual people, then semi-formal can mean a dress shirt with nice pants that aren’t khaki or chinos. Maybe a sport coat. Not a full suit. Women would be in dresses and heels, but just a little bit more subdued than semi-formal.
In the US, I’ve never seen semi-formal mean anything dressier than a suit. There may be some pockets of super-formal traditionalists out there, but you’d know if your friends were in this rare group.
Basically, wear a suit and remove the jacket if you feel over-dressed. Your wife should wear a dress (not a sundress, not a sparkly ball gown, just a fairly dressy dress that she likes), and as nice flat shoes as she can comfortably manage
I’ve never understood this. I’d be the guy in shorts… but what’s that got to do with sitting still and listening to music?
Why should I get dressed up in clothes that cost a lot of money to listen to music?
And in what way does it affect your enjoyment of the music if I wear shorts?
Nah, family’s been over here since 1630, and in California since 1848, so the opportunities are rare. Plus my great-great-great-great grandfather Jeremiah would be pissed if I were to consort with a descendant of the Tyrant. 
Oops, that should be great-great-great-great-great-great . . .
To me, semiformal is pretty low on the “dressed up list” as far as weddings go. I’ve experienced:
Black Tie (Tuxedos)
Black Tie Optional (Tux if you own one - no rentals - but you can get away with a dark suit. No brown suits)
Semi-Formal (Suits of all colors)
If you’re under 35 and unmarried, you can get away with (showing up in) no jacket for semi-formal but be prepared for some looks.
To me, semi-formal means at least jacket and tie, better to be safe with a suit. Our high-school dances in the early 90s were “semi-formals,” and that’s what I recall the dress code being. But, traditionally, semi-formal is actually a bit more formal than that.
But I wouldn’t be surprised if in Florida it meant something even more relaxed. I hate these terms because they seem to mean different things to different people. In college, we had dances called “formals,” but the dress code for those corresponded to semi-formal, if that.
I would wear a jacket and tie and be prepared to take off the jacket (especially if it was outdoors in Florida in the summer) and lose the the. It would never, ever, occur to me to wear a tux, although a suit might be in order.
I also have problems with heels in the last few years. I have to wear flats, so I do.
She should wear a nice dress and dressy flats. Flats have come a long way.
If semi-formal meant tie, then what would formal mean?
Semi-formal to me means suit with matching pants and jacket, no tie. Light colors in the morning/afternoon, dark colors after 5. A polo shirt, or even a pressed thick cotton t-shirt (not an undershirt) could be worn under the jacket. Leather shoes with a matching colored belt. Oh and remember, if you’re wearing a suit and a button-up shirt but not wearing a tie, make sure the color of the buttons match the color of the shirt. If you’re wearing a tie, this isn’t as crucial.
Black tie always refers to tuxedos.
You’re describing what I would call “business casual,” though a jacket isn’t necessary for that. See here.
Formal would be “white tie” or “black tie.” (And the latter used to be considered “semi-formal.”)
Yes, this is absolutely, unquestionably, without a doubt the textbook correct definition.
The conventional, long-standing definitions are:
Formal = white tie
Semi-formal = black tie
Lounge or informal = suit
However, nobody understands this, so words like “white tie,” “black tie,” “business dress,” “coat and tie,” etc have arisen. Plus, people like to think that they know what the terms mean even if they don’t, like people who think the word “sanguine” means “depressed” in spite of mountains of evidence to the contrary.
If I had no option to ask the hosts for clarification, I would go through the following thought process:
1a) If so, is this an evening wedding? “Yes” to 1 and 1a means I would surely assume tuxedo or very nice dark suit.
Are these the kind of people who might not be quite so fashion conscious, but still want an elegant wedding? A “yes” would mean I would assume a nice dark suit.
Are these the type of people who don’t care very much about dressing up? If “yes,” then I would assume a sport coat and tie or suit of any color to be fine.
The idea that semi-formal means button down shirt, no tie would be stretching the term so far that it is now totally, completely meaningless.
I agree with your whole flow chart, but the key point that bears repeating is that it’s ambiguous and you can’t apply your own idea of what semi-formal should mean and expect all to go well.
Stubbornly expecting the original definition to apply is every bit as silly as pretending anyone who thinks there’s such a thing as formal wear is about to dine with the queen. What matters is what the hosts have in mind.
It reveals you’re at least somewhat socially clueless and awkward. When people see you dressed inappropriately for an event, they think “Ahh, there’s someone who doesn’t understand how to dress appropriately or is too lazy to, or too poor to, or is one of those bizarre people who only seem to exist on the Straight Dope who are offended by the idea of dressing appropriately”.
I believe everyone owns pants, so in your particular example if you wear shorts they can rule out that you can’t afford to dress appropriately.
I couldn’t speculate why it bothers **NotDeadYet **, but it’s naive to think people aren’t going to notice you’re under dressed if you can only manage to look like you’re listening intently enough.
White shirt, tie, cummerbund, blazer, and no pants 
I missed this earlier. They key matter here isn’t how much one enjoys music if they are wearing certain clothes.
The key matter is that the hosts have invited guests with certain expectations. If you make the decision to reject their requests (for dress code as stated on the invitation; as well as unwritten expectations like not telling the bride that her dress really hides the extra pounds she is carrying) then you are turning an event that they are paying many, many thousands of dollars to plan to their tastes and enjoy with their friends, into an event that’s all about you and what you would rather do.
To put it in Internet terms that hopefully everyone can understand, defiantly rejecting the dress code for a friend’s wedding is the real-life version of threadshitting.
I agree with you but I think he’s speaking more to things like the Opera, a country club, a nice restaurant, etc. where one isn’t a guest so much as a customer and is footing the cost himself. Why can’t one show one’s bare legs, arms, and even toes to those venues?