Yes, a "tank top" and "vest" are actually the same thing. It's like those you can get from Calvin Klein Underwear. It's like the same thing you wear under a cardigan on cool summer days.
A vest is a type of collarless sleeveless upper-body garment. There are a variety of similar garments that may be referred to as vests, but also under other names in different regions. Vests usually fall into two broad categories:
Sleeveless upper-body garments, usually worn as undergarments, known as vests, undershirts or singlets.
Sleeveless jackets or coats, known as vests in the US and as waistcoats in the UK.
Don't you? I would have thought that Aussie and English terminology were the same. Oh well, maybe not. A vest is also a sleeveless button up bit that men wear as part of a 3-piece suit.