Working on a wedding invitation, small conflict between interested parties resulting in the need for an alternative to the wording "Semi-Formal" Attire. The conflict arises from the overall theme of the wedding being rustic. The key words would be "Not Jeans" that led to the use of semi formal in the first place.
You will find several places that define various dress code specifications, and most of them seem to be in close agreement. For instance Style-Caster or Emily Post provide this kind of information.
In your case it looks like Business Casual is a good match:
Most offices have a dress code that calls for business casual. For women, pants and a blazer or a pencil skirt and a fun blouse, is the way to go. Guys can wears slacks or chinos and a collared shirt. Absolutely no jeans or sneakers.
The problem you're going to find is that these definitions don't come to be understood as naturally as the words you might use to ask directions or order breakfast. The mere mention of business casual to some (me included) suggests work and not fun, but there you have it. Many people, I suspect, will think they know what it means. Some of them will be right and some of them will be wrong. A small fraction may look it up. A smaller fraction may wonder if you think it means the same thing that they think it means. If they love their jeans, they are going to err on the side of personal preference.
White Tie and Black Tie are something different all together. If someone doesn't know what that means, they are going to look it up and they will have no doubts that your meaning is exactly what their research tells them.
Probably cocktail attire may be a good alternative to semi-informal attire:
- A cocktail dress or cocktail gown is a woman's dress worn at cocktail parties and semi-formal or "black tie" occasions.
- These days, cocktail dress may be required for an actual cocktail party, but it’s frequently spotted at other occasions as well. You’re also likely to see this dress code pop up at weddings, anniversaries, formal birthday celebrations, certain sporting events, &c., where a little more refinement is required.
Smart casual might be another way to express the concept, but more on the informal side. The risk is that smart is subject to personal interpretations:
- Smart casual is an ambiguously-defined dress code that is generally a neat yet informal attire. The locality, type of event, context or culture constitutes the various interpretation of the dress code and therefore the designating of certain clothing pieces as smart casual is disputed—for example, jeans.