Black Tie vs. Formal

I don't think you were wrong to put formal. a lot of people don't know all of the dress code etiquette and will need clarification.

Black tie means fancy tuxes and ball gowns

No, if you want people in suits and nicer dresses I think writing formal is fine.

Personally, I think strict or traditional dress codes don't fit the way most people actually dress. For example, at least in my area and among my friends, if you wanted folks to dress up you'd want them in suits and nicer formal dresses, but that's not actually a category. It's too casual for black tie and too formal for formal. When I think of a cocktail dress, I think of something short and flirty, which isn't really my style nor is it appropriate for most weddings. However if you look at a royal wedding for example, you'll see guests in midi length dresses that sort of look like they could go from the office to brunch to a wedding and I'm pretty sure that's what "a formal cocktail dress" actually refers to. But at those same weddings men will wear tuxes, military dress, or suits, so who really knows? Anyway dress codes are VERY traditional and most contemporary couples just don't dress that way, which is why I find them always confusing on wedding invitations.

If guests ask you what to wear, just clarify with more than a few words. Tell them a suit and a nicer dress is fine!