Oh, this has turned into a thread about word choice! I love it!
A vest is a strappy sleeveless undergarment for me, too! Again, the influence of an English mother. Your vest was her waistcoat (if it was like the third piece of a three piece suit). She also said knickers for underpants, trousers for pants, jumper for sweater, plimsolls for flat canvas shoes, anorak for ski jacket, wellies for rain boots, and trainers for running shoes.
I am a home-grown Canadian, though. Of the above, I use waistcoat and wellies, and I use trousers and pants interchangeably. All the other charming English terms have not become a part of my vocabulary. I'd feel like a poseur if I said trainers instead of runners, for example. And nobody would know what I was talking about if I used the word knickers!
When I occasionally use the word vest, I'm referring to a garment worn by a small child. If I mean a similar garment made for a woman, I call it a camisole. If I'm talking about a white man's sleeveless undershirt, it's a wifebeater (a horrible yet evocative word -- if you use it, people know EXACTLY what kind of garment you're talking about!). A sleeveless top with thicker straps worn by women is a tank top.
To my French sister-in-law, culottes are women's underpants.
Until this past decade, gilet wasn't in my vocabulary. I learned it when I started getting Mini Boden catalogues in the mail when my kids were small. The catalogues sometimes had fuzzy or puffy sleeveless garments worn as outerwear that were labeled gilets. I assumed it was a European term, and pronounced it jhee-LAY.