I haven't found a good answer for this so thought I would try the fount of all knowledge - the Kitchen Table.
What is the difference between a T-shirt and a vest?
The simple answer would be that a T-shirt has short sleeves (resembling a 'T' when laid flat) and is designed to be an outer wear item, and a vest is sleeveless and designed to be an under wear item.
However, you can get vests (underwear) with short sleeves that look just the same as a T-shirt, so in that situation when does a vest become a T-shirt and change from a item of underwear to an item of outerwear?