I've never heard of the term 'singlet'. Apparently it's used in the UK, but I can honestly say I've never heard it used before. If it was a really common term I would have heard of it. Tank tops for men are called 'vests' most commonly, although 'tank top' is also sometimes used. It's different to the US where 'vest' is only used for an undershirt, in the UK we it to describe any shirt without sleeves. For sleeveless clothes for women, well there are different styles and I'm not sure of the different names. The general term would be just a 'top'.

If you're thinking of a cotton summer top, but with straps rather than sleeves, I'd call it a vest, or vest top. Singlet (not singleton!) is old-fashioned word for vest, as in the item of underwear or sportswear. I think it's mainly used in Australia now. A tank top, in GBE, is a knitted sweater without sleeves, worn over a shirt. They're usually stripey. Think 1970s Abba, and you'll get the picture.

They can be called tank tops. The only things I've heard being called singlets were for sports.